Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Main 202621 JanuaryEvening Shift
Exam
JEE Main
Year
2026
Date
21 January
Shift
Evening Shift
Subject
Mathematics
Chapter
Probability

JEE Main 2026 · 21 January · Evening Shift · Mathematics · Probability

A random variable X takes values 0,1,2,3 with probabilities (2...

A random variable XX takes values 0,1,2,30,1,2,3 with probabilities 2a+130,8a−130,4a+130,b\frac{2 a+1}{30}, \frac{8 a-1}{30}, \frac{4 a+1}{30}, b respectively, where a,b∈R\mathrm{a}, \mathrm{b} \in \mathbf{R}. Let μ\mu and σ\sigma respectively be the mean and standard deviation of X such that σ2+μ2=2\sigma^{2}+\mu^{2}=2. Then ab\frac{\mathrm{a}}{\mathrm{b}} is equal to :

Options

  1. A1212
  2. B3030
  3. C6060
  4. D3

Correct answer

C. 6060

Step-by-step solution

Sum of probabilities =1= 1: 2a+1+8a−1+4a+130+b=1⇒b=29−14a30\frac{2a+1+8a-1+4a+1}{30} + b = 1 \Rightarrow b = \frac{29-14a}{30}.
σ2+μ2=E(X2)=2\sigma^2 + \mu^2 = E(X^2) = 2.
E(X2)=8a−130+4(4a+1)30+9(29−14a)30=−102a+26430=2E(X^2) = \frac{8a-1}{30} + \frac{4(4a+1)}{30} + \frac{9(29-14a)}{30} = \frac{-102a + 264}{30} = 2.
−102a+264=60⇒a=2-102a + 264 = 60 \Rightarrow a = 2.
b=29−2830=130b = \frac{29 - 28}{30} = \frac{1}{30}.
ab=21/30=60\frac{a}{b} = \frac{2}{1/30} = 60.
Practice Probability on Quantrex Academy →

More from Probability

Suppose that Box I contains 6 red balls and 9 green balls, and Box II contains 8 red… JEE Advanced 2026A candidate has to go to the examination centre to appear in an examination. The… JEE Main 2026A bag contains 6 blue and 6 green balls. Pairs of balls are drawn without replacement… JEE Main 2026A bag contains (N+1) coins - N fair coins, and one coin with 'Head' on both sides. A coin… JEE Main 2026The probabilities that players A and B of a team are selected for the captaincy for a… JEE Main 2026A letter is known to have arrived by post either from KANPUR or from ANANTPUR. On the… JEE Main 2026From a month of 31 days, 3 different dates are selected at random. If the probability… JEE Main 2026A coin is tossed 8 times. If the probability that exactly 4 heads appear in the first six… JEE Main 2026A man throws a fair coin repeatedly. He gets 10 points for each head he throws and 5… JEE Main 2026The probability distribution of a random variable X is given below : (array… JEE Main 2026A bag contains 10 balls out of which k are red and ( 10-k ) are black, where 0 ≤ k ≤ 10 .… JEE Main 2026Let S be a set of 5 elements and P(S) denote the power set of S. Let E be an event of… JEE Main 2026From a lot containing 10 defective and 90 non-defective bulbs, 8 bulbs are selected one… JEE Main 2026Bag A contains 9 white and 8 black balls, while bag B contains 6 white and 4 black balls.… JEE Main 2026From the first 100 natural numbers, two numbers first a and then b are selected randomly… JEE Main 2026If a random variable x has the probability distribution array |c|c|c|c|c|c|c|c|c| x & 0 &… JEE Main 2026 Full Probability list Probability JEE Maths PYQsJEE Mathematics PYQs All JEE Main PYQs