# Question

With reference to Exercise 3.24, find the distribution function of Z and draw its graph.

In exercise

The probability density of the random variable Z is given by

In exercise

The probability density of the random variable Z is given by

## Answer to relevant Questions

The density function of the random variable X is given by Find P(X < 1/4 ) and P(X > 1/2). With reference to Exercise 3.28, find P(0.8< X < 1.2) using (a) The probability density; (b) The distribution function. For each of the following, determine c so that the function can serve as the probability distribution of a random variable with the given range: (a) f(x) = cx for x = 1, 2, 3, 4, 5; (b) (c) f(x) = cx2 for x = 1, 2, 3, . . . ...F(x, y) is the value of the joint distribution function of two discrete random variables X and Y at (x, y), show that (a) F(-∞,-∞) = 0; (b) F(q, q) = 1; (c) if a< b and c< d, then F(a, c) ≤ F(b, d). Use the formula obtained in Exercise 3.58 to verify the result, 0.074, of Example 3.17. In exercise If F(x, y) is the value of the joint distribution function of the two continuous random variables X and Y at (x, y), express ...Post your question

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