The probability distribution table of a random variable X is given below., X_i, P(X_i), 0, 1/8, 1, a, 2, b, 3, 1/8, If E(X) = 3/2, then the values of a and b are: Option 1: 3/8 and 3/8 respectively Option 2: 2/8 and 1/2 respectively Option 3: 1/2 and 2/8 respectively Option 4: 1/8 and 5/8 respectively

Answer: 3/8 and 3/8 respectively. Solution: Probabilities sum to 1, giving a+b = 3/4. From E(X) = a+2b+3/8 = 3/2 we get a+2b = 9/8. Subtracting gives b = 3/8 and hence a = 3/8.

Algebra

Probability

Medium

applied

The probability distribution table of a random variable X is given below.

$X_i$ $P(X_i)$
0 1/8
1 a
2 b
3 1/8

If $E(X) = \dfrac{3}{2}$ , then the values of a and b are:

$X_i$	$P(X_i)$
0	1/8
1	a
2	b
3	1/8

$\dfrac{3}{8}$ and $\dfrac{3}{8}$ respectively

$\dfrac{2}{8}$ and $\dfrac{1}{2}$ respectively

$\dfrac{1}{2}$ and $\dfrac{2}{8}$ respectively

$\dfrac{1}{8}$ and $\dfrac{5}{8}$ respectively

✅ Correct Option: 1

Probabilities sum to $1$ , giving $a+b = \frac{3}{4}$ . From $E(X) = a+2b+\frac{3}{8} = \frac{3}{2}$ we get $a+2b = \frac{9}{8}$ . Subtracting gives $b = \frac{3}{8}$ and hence $a = \frac{3}{8}$ .

2025: 3 June Shift 2

The probability distribution of a random variable X is

X	0	1	2	3	4
P(X)	0.2	k	k	2k	k

Match List-I with List-II

List-I	List-II
(A) value of k	(I) $\frac{16}{25}$
(B) $P(x \geq 2)$	(II) $\frac{9}{25}$
(C) $P(x = 3)$	(III) $\frac{4}{25}$
(D) $P(x < 2)$	(IV) $\frac{8}{25}$

Choose the correct answer from the options given below:

2025: 22 May Shift 2

If $P(A) = \frac{3}{10}$ , $P(B) = \frac{2}{5}$ and $P(A \cup B) = \frac{3}{5}$ then the value of $P(B|A) + P(A|B)$ is:

2023: 15 June Shift 2

The mean of the number of heads in a simultaneous toss of three coins is :

2022: 23 Aug Shift 1

The probability of answering a question correctly, is :

2025: 15 May Shift 2

If the probability that an individual suffers a bad reaction from an injection of a given serum is 0.001. The probability that out of 2000 individuals, more than two individuals suffer from bad reaction is:

[Given that $e^{-2} \approx 0.13534$ ]

2025: 29 May Shift 2

Let A and B be two events. Then which of the following statements are TRUE?

(A) $P(B|A) = \frac{P(A \cap B)}{P(A)}$ , provided $P(A) \neq 0$

(B) $P(B') = 1 + P(B)$

(D) $P(A \cap B) = P(A).P(B)$ If A and B are independent events

Choose the correct answer from the options given below:

The probability distribution table of a random variable X is given below. XiX_iXi​P(Xi)P(X_i)P(Xi​)01/81a2b31/8 If E(X)=32E(X) = \dfrac{3}{2}E(X)=23​, then the values of a and b are:

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

The probability distribution table of a random variable X is given below.

$X_i$ $P(X_i)$
0 1/8
1 a
2 b
3 1/8

If $E(X) = \dfrac{3}{2}$ , then the values of a and b are: