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

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:

Table

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: