If the mean and variance of the data 65,68,58,44 , 48,45,60, α, β, 60 where α β are 56 and 66.2 respectively, then α 2 +β 2 is equal to

Mathematics · Probability

JEE Main 2024 — 29 January, Shift 1 — Question 26

If the mean and variance of the data $65,68,58,44$ , $48,45,60, \alpha, \beta, 60$ where $\alpha>\beta$ are 56 and 66.2 respectively, then $\alpha^{2}+\beta^{2}$ is equal to

Answer: 6344

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Step-by-step solution

Sol. $\overline{\mathrm{x}}=56$

$\sigma^{2}=66.2$

$\Rightarrow \frac{\alpha^{2}+\beta^{2}+25678}{10}-(56)^{2}=66.2$

$\therefore \alpha^{2}+\beta^{2}=6344$

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Exam: JEE Main 2024
Paper: 29 January, Shift 1
Subject: Mathematics
Chapter: Probability
Topic: Mean, variance, expected values of distributions

A fair die is thrown until 2 appears. Then the probability, that 2 appears in even number of throws, is

Answer: 6344

Step-by-step solution

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