# Question: The probability density of the random variable Z is given

The probability density of the random variable Z is given by

Find k and draw the graph of this probability density.

Find k and draw the graph of this probability density.

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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 Verify that f(x) = 2x/k(k+ 1) for x = 1, 2, 3, . . . , k can serve as the probability distribution of a random variable with the given range. With reference to Figure 3.9, find expressions for the values of the distribution function of the mixed random variable X for (a) x ≤ 0; (b) 0< x< 0.5; (c) 0.5 F x< 1; (d) x ≥ 1. Figure 3.9 If the joint probability distribution of X and Y is given by f(x, y) = 1/30 (x+ y) for x = 0, 1, 2, 3; y = 0, 1, 2 Construct a table showing the values of the joint distribution function of the two random variables at the ...Use the joint probability density obtained in Exercise 3.56 to find P(X + Y > 3). In exercisePost your question