# Question

Use the transformation technique to rework Exercise 7.2.

In exercise

If the probability density of X is given by

And Y = X2

In exercise

If the probability density of X is given by

And Y = X2

## Answer to relevant Questions

If the probability density of X is given by Where k is an appropriate constant, find the probability density of the random variable Y = 2X / 1+ 2X . Identify the distribution of Y, and thus determine the value of k. Consider the random variable X with the probability density (a) Use the result of Example 7.2 to find the probability density of Y = | X|. (b) Find the probability density of Z = X2(=Y2). If X1 and X2 are independent random variables having binomial distributions with the respective parameters n1 and θ and n2 and θ, show that Y = X1 + X2 has the binomial distribution with the parameters n1 + n2 and θ. Let X1 and X2 be two continuous random variables having the joint probability density Find the joint probability density of Y1 = X21 and Y2 = X1X2. If n independent random variables Xi have normal distributions with the means µi and the standard deviations σi, find the moment-generating function of their sum and identify the corresponding distribution, its mean, and ...Post your question

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