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) If X and Y are two independent random variables, then show that: 4/6 Var (X+Y) = Var (X) + Var (Y)

) If X and Y are two independent random variables, then show that: 4/6 Var (X+Y) = Var (X) + Var (Y)

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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3016- -(P-4)(Q-9)(20) Marks in Economics Marks in Maths (4) 78 36 98 25 75 82 90 62 65 39 81 51 91 60 68 62 86 58 53 47 (f) Find the least value of r in a sample of 18 pairs of observations from a bivariate normal population, significant at 5% level of significance. (a) There are two bags. The first bag contains 10 white and 3 black balls and second bag contains 3 white and 5 black balls. Two balls are drawn at random 5° from the first bag and put into second bag. Then a ball is drawn from second bag. Find the 13 probability that the ball drawn is a white ball. (b) If X and Y are two independent random variables, then show that: 4/6 Var (X+Y) = Var (X) + Var (Y) (a) For a random variable X with mean μ = 10 and variance o² = 4, apply Chebyshev's inequality to calculate : -(P-4)(Q-9)(20) (i) P(5 < X < 15) (ii) P(|X-10| ≥3) (iii) P(|X-10| <3) b) A car hire firm has two cars, which it hires out day by day. The number of demands for a car on each day is distributed as a Poisson variate with mean 1.5. Calculate the proportion of days on which : 0.2231 (i) neither car is used (ii) some demand is refused 1912625 (2) ...
Transcribed Image Text:3016- -(P-4)(Q-9)(20) Marks in Economics Marks in Maths (4) 78 36 98 25 75 82 90 62 65 39 81 51 91 60 68 62 86 58 53 47 (f) Find the least value of r in a sample of 18 pairs of observations from a bivariate normal population, significant at 5% level of significance. (a) There are two bags. The first bag contains 10 white and 3 black balls and second bag contains 3 white and 5 black balls. Two balls are drawn at random 5° from the first bag and put into second bag. Then a ball is drawn from second bag. Find the 13 probability that the ball drawn is a white ball. (b) If X and Y are two independent random variables, then show that: 4/6 Var (X+Y) = Var (X) + Var (Y) (a) For a random variable X with mean μ = 10 and variance o² = 4, apply Chebyshev's inequality to calculate : -(P-4)(Q-9)(20) (i) P(5 < X < 15) (ii) P(|X-10| ≥3) (iii) P(|X-10| <3) b) A car hire firm has two cars, which it hires out day by day. The number of demands for a car on each day is distributed as a Poisson variate with mean 1.5. Calculate the proportion of days on which : 0.2231 (i) neither car is used (ii) some demand is refused 1912625 (2) ...
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