Stats Question Suppose a random variable X has a probability distribution given

Question

Stats Question

Suppose a random variable X has a probability distribution given by: A single experiment generates a random value from this distribution. If the experiment is repeated many times: What will be the approximate proportion of times that the value is -1? Give a reason for your answer. What will be the approximate value of the sample mean of these random variables? Give a reason for your answer Calculate the mean and variance of this distribution. Let Y = 3X - 2. What are the rules that relate the mean and variance of Y to the mean and variance of X? Use these rules to find the mean and variance of y.

Explanation / Answer

(i)Approximate proportion for x=-1 is 0.3=3/10

This is because of the law of large numbers.

(ii)Mean=-1*0.3+2*0.7=1.1

b)Mean=1.1

Variance=0.3*(-1-1.1)^2+0.7*(2-1.1)^2= 1.89

c)Y=2X-2

E[Y]=2*1.1-2=0.2

V[Y]=4*1.89=7.56

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