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Questions without answers in Probability and Statistics
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1
GATE Civil 2021 Set 1 | Question: 3
The shape of the cumulative distribution function of Gaussian distribution is Horizontal line Straight line at $45$ degree angle Bell-shaped $S$-shaped
The shape of the cumulative distribution function of Gaussian distribution isHorizontal lineStraight line at $45$ degree angleBell-shaped$S$-shaped
Arjun
13.0k
points
Arjun
asked
Feb 19, 2021
Probability and Statistics
gatecivil-2021-set1
probability-and-statistics
statistics
gaussian-distributions
+
–
0
votes
0
answers
2
GATE2020 CE-2-18
A fair (unbiased) coin is tossed $15$ times. The probability of getting exactly $8$ Heads (round off to three decimal places), is _______.
A fair (unbiased) coin is tossed $15$ times. The probability of getting exactly $8$ Heads (round off to three decimal places), is _______.
go_editor
5.3k
points
go_editor
asked
Feb 13, 2020
Probability and Statistics
gate2020-ce-2
numerical-answers
probability-and-statistics
probability
+
–
0
votes
0
answers
3
GATE2017 CE-2-20
A two-faced fair coin has its faces designated as head (H) and tail (T). This coin is tossed three times in succession to record the following outcomes: H, H, H. If the coin is tossed one more time, the probability (up to one decimal place) of obtaining H again, given the previous realizations of H, H and H, would be ________
A two-faced fair coin has its faces designated as head (H) and tail (T). This coin is tossed three times in succession to record the following outcomes: H, H, H. If the c...
gatecse
4.0k
points
gatecse
asked
Aug 7, 2019
Probability and Statistics
gate2017-ce-2
numerical-answers
probability-and-statistics
probability
conditional-probability
+
–
0
votes
0
answers
4
GATE2019 CE-1: 23
The probability that the annual maximum flood discharge will exceed $25000 \: m^3/s$, at least once in next $5$ years is found to be $0.25$. The return period of this flood event (in years, round off to $1$ decimal place is __________
The probability that the annual maximum flood discharge will exceed $25000 \: m^3/s$, at least once in next $5$ years is found to be $0.25$. The return period of this flo...
Arjun
13.0k
points
Arjun
asked
Feb 14, 2019
Probability and Statistics
gate2019-ce-1
numerical-answers
probability-and-statistics
probability
conditional-probability
+
–
0
votes
0
answers
5
GATE2019 CE-2: 26
The probability density function of a continuous random variable distributed uniformly between $x$ and $y$ (for $y>x$) is $\dfrac{1}{x-y}$ $\dfrac{1}{y-x}$ $x-y$ $y-x$
The probability density function of a continuous random variable distributed uniformly between $x$ and $y$ (for $y>x$) is$\dfrac{1}{x-y}$$\dfrac{1}{y-x}$$x-y$$y-x$
Arjun
13.0k
points
Arjun
asked
Feb 12, 2019
Probability and Statistics
gate2019-ce-2
probability-and-statistics
probability
probability-density-function
random-variable
uniform-distribution
+
–
0
votes
0
answers
6
GATE2016-2-1
The spot speeds (expressed in km/hr) observed at a road section are $66, 62, 45, 79, 32, 51, 56, 60, 53,$ and $49$. The median speed (expressed in km / hr) is ______ (Note: answer with one decimal accuracy)
The spot speeds (expressed in km/hr) observed at a road section are $66, 62, 45, 79, 32, 51, 56, 60, 53,$ and $49$. The median speed (expressed in km / hr) is ______(Note...
Milicevic3306
11.9k
points
Milicevic3306
asked
Mar 27, 2018
Probability and Statistics
gate2016-ce-2
numerical-answers
probability-and-statistics
statistics
mean-median-mode
+
–
0
votes
0
answers
7
GATE2016-2-4
$X$ and $Y$ are two random independent events. It is known that $P(X)=0.40$ and $P(X \cup Y^C)=0.7$. Which one of the following is the value of $P(X \cup Y)$? $0.7$ $0.5$ $0.4$ $0.3$
$X$ and $Y$ are two random independent events. It is known that $P(X)=0.40$ and $P(X \cup Y^C)=0.7$. Which one of the following is the value of $P(X \cup Y)$?$0.7$$0.5$$0...
Milicevic3306
11.9k
points
Milicevic3306
asked
Mar 27, 2018
Probability and Statistics
gate2016-ce-2
probability-and-statistics
probability
independent-events
+
–
1
votes
0
answers
8
GATE2016-2-27
If $f(x)$ and $g(x)$ are two probability density functions, $f(x) = \begin{cases} \dfrac{x}{a}+1 & :-a \leq x < 0 \\ -\dfrac{x}{a}+1 & : 0 \leq x \leq a \\ 0 & :\text{otherwise} \end{cases}$ ... different; Variance of $f(x)$ and $g(x)$ are same Mean of $f(x)$ and $g(x)$ are different; Variance of $f(x)$ and $g(x)$ are different
If $f(x)$ and $g(x)$ are two probability density functions,$f(x) = \begin{cases} \dfrac{x}{a}+1 & :-a \leq x < 0 \\ -\dfrac{x}{a}+1 & : 0 \leq x \leq a \\ 0 & :\text{oth...
Milicevic3306
11.9k
points
Milicevic3306
asked
Mar 27, 2018
Probability and Statistics
gate2016-ce-2
probability-and-statistics
probability
probability-density-function
variance
+
–
0
votes
0
answers
9
GATE2016-1-4
Type II error in hypothesis testing is acceptance of the null hypothesis when it is false and should be rejected rejection of the null hypothesis when it is true and should be accepted rejection of the null hypothesis when it is false and should be rejected acceptance of the null hypothesis when it is true and should be accepted
Type II error in hypothesis testing isacceptance of the null hypothesis when it is false and should be rejectedrejection of the null hypothesis when it is true and should...
Milicevic3306
11.9k
points
Milicevic3306
asked
Mar 27, 2018
Probability and Statistics
gate2016-ce-1
probability-and-statistics
statistics
hypothesis-testing
+
–
0
votes
0
answers
10
GATE2016-1-26
Probability density function of a random variable $X$ is given below $f(x) = \begin{cases} 0.25 & \text{ if } 1 \leq x \leq 5 \\ 0 & \text{ otherwise} \end{cases}$ $P(X \leq 4)$ is $\dfrac{3}{4} \\$ $\dfrac{1}{2} \\$ $\dfrac{1}{4} \\$ $\dfrac{1}{8}$
Probability density function of a random variable $X$ is given below$$f(x) = \begin{cases} 0.25 & \text{ if } 1 \leq x \leq 5 \\ 0 & \text{ otherwise} \end{cases}$$$P(X \...
Milicevic3306
11.9k
points
Milicevic3306
asked
Mar 27, 2018
Probability and Statistics
gate2016-ce-1
probability-and-statistics
probability
probability-density-function
random-variable
+
–
0
votes
0
answers
11
GATE2017 CE-1: 2
The number of parameters in the univariate exponential and Gaussian distributions, repsectively, are $2$ and $2$ $1$ and $2$ $2$ and $1$ $1$ and $1$
The number of parameters in the univariate exponential and Gaussian distributions, repsectively, are$2$ and $2$$1$ and $2$$2$ and $1$$1$ and $1$
Milicevic3306
11.9k
points
Milicevic3306
asked
Mar 26, 2018
Probability and Statistics
gate2017-ce-1
probability-and-statistics
probability
gaussian-distributions
+
–
0
votes
0
answers
12
GATE2017 CE-1: 26
For the function $f(x)=a+bx,0\leq x\leq1,$ to be a valid probability density function,which one of the following statements is correct? $a=1,b=4$ $b=0.5,b=1$ $a=0,b=1$ $a=1,b=-1$
For the function $f(x)=a+bx,0\leq x\leq1,$ to be a valid probability density function,which one of the following statements is correct?$a=1,b=4$$b=0.5,b=1$$a=0,b=1$$a=1,b...
Milicevic3306
11.9k
points
Milicevic3306
asked
Mar 26, 2018
Probability and Statistics
gate2017-ce-1
probability-and-statistics
probability
probability-density-function
+
–
0
votes
0
answers
13
GATE2015-2-26
The probability density function of a random variable, $x$ is $f(x)= \begin{cases} \dfrac{x}{4} ( 4-x^2) & \text{ for } 0 \leq x \leq 2 \\ 0 & \text{ otherwise} \end{cases}$ The mean $\mu _x$ of the random variable is ______.
The probability density function of a random variable, $x$ is$f(x)= \begin{cases} \dfrac{x}{4} ( 4-x^2) & \text{ for } 0 \leq x \leq 2 \\ 0 & \text{ otherwise} \end{ca...
Milicevic3306
11.9k
points
Milicevic3306
asked
Mar 26, 2018
Probability and Statistics
gate2015-ce-2
numerical-answers
probability-and-statistics
probability
probability-density-function
+
–
0
votes
0
answers
14
GATE2015-1-3
Consider the following probability mass function (p.m.f) of a random variable $X:$ $p(x,q) = \begin{cases} q & \text{ if } X=0 \\ 1 – q & \text{ if } X=1 \\ 0 & \text{otherwise} \end{cases} $ If $q=0.4$, the variance of $X$ is _________
Consider the following probability mass function (p.m.f) of a random variable $X:$$$p(x,q) = \begin{cases} q & \text{ if } X=0 \\ 1 – q & \text{ if } X=1 \\ 0 & \text{o...
Milicevic3306
11.9k
points
Milicevic3306
asked
Mar 26, 2018
Probability and Statistics
gate2015-ce-1
numerical-answers
probability-and-statistics
probability
probability-mass-function
random-variable
+
–
0
votes
0
answers
15
GATE2014-2-5
If $\{x\}$ is a continuous, real valued random variable defined over the interval $(- \infty, + \infty)$ and its occurrence is defined by the density function given as: $f(x) = \dfrac{1}{\sqrt{2 \pi} *b} e^{-\frac{1}{2} (\frac{x-a}{b})^2}$ where $'a'$ and $b'$ are the statistical ... $1$ $0.5$ $\pi$ $\dfrac{\pi}{2}$
If $\{x\}$ is a continuous, real valued random variable defined over the interval $(- \infty, + \infty)$ and its occurrence is defined by the density function given as: $...
Milicevic3306
11.9k
points
Milicevic3306
asked
Mar 25, 2018
Probability and Statistics
gate2014-ce-2
probability-and-statistics
probability
probability-density-function
random-variable
+
–
0
votes
0
answers
16
GATE2014-2-1
A fair (unbiased) coin was tossed four times in succession and resulted in the following outcomes: (i) Head, (ii) Head, (iii) Head, (iv) Head. The probability of obtaining a ‘Tail’ when the coin is tossed again is $0$ $\dfrac{1}{2} \\$ $\dfrac{4}{5} \\$ $\dfrac{1}{5}$
A fair (unbiased) coin was tossed four times in succession and resulted in the following outcomes: (i) Head, (ii) Head, (iii) Head, (iv) Head. The probability of obtainin...
Milicevic3306
11.9k
points
Milicevic3306
asked
Mar 25, 2018
Probability and Statistics
gate2014-ce-2
probability-and-statistics
probability
conditional-probability
+
–
0
votes
0
answers
17
GATE2014-1-3
The probability density function of evaporation $E$ on any day during a year in a watershed is given by $f(E) = \begin{cases} \dfrac{1}{5} & 0 \leq E \leq 5\: \text{mm/day} \\ 0 & \text{otherwise} \end{cases}$ The probability that $E$ lies in between $2$ and $4$ mm/day in a day in the watershed is (in decimal) ____________
The probability density function of evaporation $E$ on any day during a year in a watershed is given by$f(E) = \begin{cases} \dfrac{1}{5} & 0 \leq E \leq 5\: \text{mm/day...
Milicevic3306
11.9k
points
Milicevic3306
asked
Mar 25, 2018
Probability and Statistics
gate2014-ce-1
numerical-answers
probability-and-statistics
probability
probability-density-function
+
–
0
votes
0
answers
18
GATE Civil 2013 | Question: 29
Find the value of $\lambda$ such that the function $f(x)$ is a valid probability density function _______ $f(x) = \begin{cases} \lambda (x-1)(2-x) & \text{for } 1 \leq x \leq 2 \\ 0 & \text{otherwise} \end{cases}$
Find the value of $\lambda$ such that the function $f(x)$ is a valid probability density function _______$f(x) = \begin{cases} \lambda (x-1)(2-x) & \text{for } 1 \leq x \...
Milicevic3306
11.9k
points
Milicevic3306
asked
Mar 25, 2018
Probability and Statistics
gate2013-ce
numerical-answers
probability-and-statistics
probability
probability-density-function
+
–
0
votes
0
answers
19
GATE Civil 2013 | Question: 3
A $1$-h rainfall of $10$ cm magnitude at a station has a return period of $50$ years. The probability that a $1$-h rainfall of magnitude $10$ cm or more will occur in each of two successive years is $0.04$ $0.2$ $0.02$ $0.0004$
A $1$-h rainfall of $10$ cm magnitude at a station has a return period of $50$ years. The probability that a $1$-h rainfall of magnitude $10$ cm or more will occur in eac...
Milicevic3306
11.9k
points
Milicevic3306
asked
Mar 25, 2018
Probability and Statistics
gate2013-ce
probability-and-statistics
probability
+
–
0
votes
0
answers
20
GATE Civil 2012 | Question: 27
In an experiment, positive and negative values are equally likely to occur. The probability of obtaining at most one negative value in five trials is $\dfrac{1}{32} \\$ $\dfrac{2}{32} \\$ $\dfrac{3}{32} \\$ $\dfrac{6}{32}$
In an experiment, positive and negative values are equally likely to occur. The probability of obtaining at most one negative value in five trials is$\dfrac{1}{32} \\$$\d...
Milicevic3306
11.9k
points
Milicevic3306
asked
Mar 25, 2018
Probability and Statistics
gate2012-ce
probability-and-statistics
probability
+
–
0
votes
0
answers
21
GATE Civil 2012 | Question: 2
The annual precipitation data of a city is normally distributed with mean and standard deviation as $1000$ mm and $200$ mm, respectively. The probability that the annual precipitation will be more than $1200$ mm is $<50 \%$ $50 \%$ $75 \%$ $100\%$
The annual precipitation data of a city is normally distributed with mean and standard deviation as $1000$ mm and $200$ mm, respectively. The probability that the annual ...
Milicevic3306
11.9k
points
Milicevic3306
asked
Mar 25, 2018
Probability and Statistics
gate2012-ce
probability-and-statistics
probability
normal-distribution
+
–
0
votes
0
answers
22
GATE2018 CE-2: 19
Probability (up to one decimal place) of consecutively picking $3$ red balls without replacement from a box containing $5$ red balls and $1$ white ball is ___________
Probability (up to one decimal place) of consecutively picking $3$ red balls without replacement from a box containing $5$ red balls and $1$ white ball is ___________
gatecse
4.0k
points
gatecse
asked
Feb 17, 2018
Probability and Statistics
gate2018-ce-2
probability-and-statistics
probability
conditional-probability
numerical-answers
+
–
0
votes
0
answers
23
GATE2018 CE-2: 2
The graph of a function $f(x)$ is shown in the figure. For $f(x)$ to be a valid probability density function, the value of $h$ is $1/3$ $2/3$ $1$ $3$
The graph of a function $f(x)$ is shown in the figure.For $f(x)$ to be a valid probability density function, the value of $h$ is$1/3$$2/3$$1$$3$
gatecse
4.0k
points
gatecse
asked
Feb 17, 2018
Probability and Statistics
gate2018-ce-2
probability-and-statistics
probability
probability-density-function
+
–
0
votes
0
answers
24
GATE2018 CE-2: 3
A probability distribution with right skew is shown in the figure. The correct statement for the probability distribution is Mean is equal to mode Mean is greater than median but less than mode Mean is greater than median and mode Mode is greater than median
A probability distribution with right skew is shown in the figure.The correct statement for the probability distribution isMean is equal to modeMean is greater than media...
gatecse
4.0k
points
gatecse
asked
Feb 17, 2018
Probability and Statistics
gate2018-ce-2
probability-and-statistics
statistics
probability-distribution
mean-median-mode
+
–
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