group of 10 people, their are 4 girls and 6 boys. If a sample of 3 people is chosen at random. Find the expected number of boys chosen?

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Q 1(a) If X and Y are two independent normal random variables with mean O and deviation of 2  Prove (by using the convolution of density functions) that Z X + Y is also a normal random variable, Also, find the mean and standard deviation of Z. 

(b) In a group of 10 people, their are 4 girls and 6 boys. If a sample of 3 people is chosen at random. Find the expected number of boys chosen?

Q 2 The time (in hours) to repair a machine A is exponentially distributed random variable X with mean ¡ and the time (in hours) to repair a machine B is eponentia]ly distributed random variable Y ith mean 1/2, Find (a) Probability density function of Z = X-Y (b) Find the probability that repair time for machine A is at most 3 hours more than the repair time for machine B. 

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