# Question: Find the distribution function of the random variable X whose

Find the distribution function of the random variable X whose probability density is given by

Also sketch the graphs of the probability density and distribution functions.

Also sketch the graphs of the probability density and distribution functions.

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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 Exercise 3.34, find the probability density of Y and use it to recalculate the two probabilities. In exercise Find P(Y ≤ 5) and P(Y > 8). With reference to Exercise 3.42, find the following values of the joint distribution function of the two random variables: (a) F(1.2, 0.9); (b) F(- 3, 1.5); (c) F(2, 0); (d) F(4, 2.7). In exercise If the joint probability density of X and Y is given by Find the probability that the sum of the values of X and Y will exceed 1/2 . With reference to Exercise 3.62, In exercise Find k if the joint probability distribution of X, Y, and Z is given by f(x,y,z) = kxyz For x = 1, 2; y = 1, 2, 3; z = 1, 2. Find (a) P(X = 1, Y ≤ 2, Z = 1); (b) P(X = 2, Y + ...Post your question