# Question: The distribution function of the random variable X is given

The distribution function of the random variable X is given by

Find P(X ≤ 2), P(1< X < 3), and P(X > 4).

Find P(X ≤ 2), P(1< X < 3), and P(X > 4).

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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 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 (a) P(X ≤ 1/2 , Y ≤ 1/2 ); (b) P(X + Y > 2/3 ); (c) P(X > 2Y). Use the formula obtained in Exercise 3.58 to verify the result of Exercise 3.57. 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 P(a < ...With reference to Example 3.20, find (a) the marginal distribution function of X, that is, the function given by G(x) = P(X F x) for - ∞ < x < ∞; (b) the conditional distribution function of X given Y = 1, that is, the ...Post your question