Checking my answers 6.9: y: -1,0,3 and p(y): 0.2, 0.4, 0.4 6.10: p(y) = -(y^(1/2

Question

Checking my answers 6.9: y: -1,0,3 and p(y): 0.2, 0.4, 0.4 6.10: p(y) = -(y^(1/2)-1)/(3y^(1/2)) 6.11: 6.9 The random variable X has a distribution given by the table 1 0 1 2 px)0.1 0.2 0.3 0.4 Find the distribution of a random variable Y X2-1. 6.10 Let X be a continuous random variable with density /(x) =(x + 1) for 0 $15 1 elsewhere Find the density of the random variable Y = X2. 6.11 Use the methods of this section to show that linear functions of normal random variables again have a normal distribution and variance 2. How do the rnean and variance of y relate to those of X? Again, use the methods of this section. . Let Y = a + bX, where X is normal with the mean

Explanation / Answer

6.9:

Following table shows the calculations:

So pdf of Y is

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6:10 is also correct.

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6:11 This questions days "method of this section" ...

X p(x) Y=x^2-1 -1 0.1 0 0 0.2 -1 1 0.3 0 2 0.4 3

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