List of top Mathematics Questions on Probability Distribution asked in CUET (UG)

If a random variable \(X\) has probability distribution \[ P(X=x)=kx, \] \[ x=1,2,3,4, \] then the value of \(k\) is:

A random variable \( X \) has the following probability distribution:

X	0	1	2	otherwise
P(X)	k	2k	3k	0

Then:
(A) \( k = \frac{1}{6} \)
(B) \( P(X < 2) = \frac{1}{2} \)
(C) \( E(X) = \frac{3}{4} \)
(D) \( P(1 < X \leq 2) = \frac{5}{6} \)
Choose the correct answer from the options given below:

A random variable \( X \) has the following probability distribution:

X	0	1	2	3	4	5	6	7
P(X)	0	m	2m	2m	3m	m²	2m²	7m² + m

The value of m is:

A random variable X has the following probability distribution:

X	1	2	3	4	5	6	7
P(X)	k	2k	2k	3k	k²	2k²	7k² + k

Match the options of List-I to List-II:

List-I	List-II
(A) k	(I) 7/10
(B) P(X < 3)	(II) 53/100
(C) P(X ≥ 2)	(III) 1/10
(D) P(2 < X ≤ 7)	(IV) 3/10

Choose the correct answer from the options given below.

If the random variable X has the following distribution:

X	0	1	2	otherwise
P(X)	k	2k	3k	0

Match List-I with List-II:

Choose the correct answer from the options given below:

For the following probability distribution:

X	3	4	5
P(X)	0.5	0.2	0.3

The mean, variance, and standard deviation respectively are:

Match List I with List II

	LIST I		LIST II
A.	A special characteristic of a population is called	I.	Sample Size
B.	The number of statistical individuals in a sample is called	II.	Statistic
C.	A special characteristic of a sample is called	III.	Standard error
D.	The standard deviation of the sampling distribution of a statistic is known as its	IV.	Parameter

Choose the correct answer from the options given below:

A random variable X has the following probability distribution

X	0	1	2	3	4	5	6	7
P(X)	0	k	2k	2k	3k	k²	2k²	7k²+k

then value of E(X) is:

Which of the following can be the probability distribution of a random variable ?

A random variable has the following probability distribution

\(X=x_i\)	2	3	4	5
\(P(X=x_i)\)	4k	k	5k	2k

The value of P(X <3) is:

If the mean of the probability distribution is 5, then the value of k is:

X	2	k	5
P(X)	0.2	0.4	0.6

For a discrete random variable X, whose probability distribution is defined as :
\(P(x)=\begin{cases} 2k(x+1) ;& x = 0,1 \\ 3kx; & x=2 \\ k(5-x) & x=3 \end{cases}\)
The value of mean will be

The random variable X has a probability distribution P(X) of the following form, where k is some number.

\[P(X=x) \begin{cases} k & \quad \text{if } x=0\\ 2k & \quad \text{if } \text{ x=1}\\ 3k & \quad \text{if } \text{ x=2} \\ 0 & \quad \text{otherwise} \end{cases}\]

Then P(x≤2) is:

Which of the following are not the probability distribution of a random variable ?
A.

X	0	1	2
P(X)	0.4	0.4	0.2

B.

X	0	1	2	3	4
P(X)	0.4	0.4	0.2	-0.1	0.3

C.

Y	-1	0	1
P(Y)	0.6	0.1	0.2

D.

Z	3	2	1	0	-1
P(Z)	0.3	0.2	0.4	0.1	0.05

E.

X	0	1	2
P(X)	\(\frac{25}{36}\)	\(\frac{10}{36}\)	\(\frac{1}{36}\)

Choose the correct answer from the options given below :

Consider the following statements with respect to probability distributions :
A. When mean (μ) = 1 and standard deviation (σ) = 0 for a data set, normal distribution is called standard normal distribution.
B. In a normal distribution of data, z is given by \(z=\frac{\mu-x}{\sigma}\)
C. P('t' success) is the (r + 1)^th term in the binomial expansion of (q + p)ⁿ.
D. In a random experiment, a collection of trials is called Bernoulli, if trials are department by nature.
E. When a random variable whose value is obtained by measuring and it takes many values between two values, it is called a continuous random variable.
Choose the correct answer from the options given below :

Which of the following statements are true ?
(A) Central limit theorem states that the sampling distribution of the mean (\(\bar x\)) approaches a normal distribution as the sample size increases.
(B) As per Central Limit Theorem, when the sample size increases, the mean (\(\bar x\)) for the data becomes closer to the mean of overall population.
(C) The shape of t-distribution does not depend on degree of freedom.
Choose the correct answer from the options given below :

The probability distribution of a discrete random variable \(X\) is given below :

\(X\)	\(2\)	\(3\)	\(4\)	\(5\)
\(P(X)\)	\(\frac5k\)	\(\frac7k\)	\(\frac9k\)	\(\frac{11}{k}\)

then the value of k is:

A discrete random variable X has the following probability distribution:

X:	0	1	2	3	4	5
P(X):	b	3b	5b	3b	4b	6b

The value of b is:

Two cards are drawn without replacement. The probability distribution of number of aces is given by:

A discrete random variable X takes the values 0, 1, 2, 3, 4 and its mean is 1.6. If P(X=1)=0.4, P(X=4)=P(X=2) and P(X=3)=2P(X=2), then P(X=0) is:

The probability distribution of a discrete random variable X is defined as:
\(P(X=x)=\begin{cases} 3kx & \text{for } x=1,2,3\\ 5k(x+2) & \text{for } x=4,5 \\ 0& \text{otherwise}\end{cases}\)
The mean of the distribution is:

If a discrete random variable X has the following probability distribution:

X	\(\frac{2}{3}\)	1	\(\frac{4}{3}\)
P(X)	\(c^2\)	\(c^2\)	c

then c is:

A discrete random variable X has the following probability distribution:

X	1	2	3	4	5	6
P(X)	\(\frac{2}{k}\)	\(\frac{4}{k}\)	\(\frac{1}{k}\)	\(\frac{2}{k}\)	\(\frac{3}{k}\)	\(\frac{5}{k}\)

The value of k is: