Suppose that the random variable X has the following cumulative distribution function.F(x) =x < 24) 2 ≤ x < 3x > 3{fc²_(a) Find P(X> 2.50)(b) Find P(1.16 < X < 2.09)(c) Find the mean of X.(d) Find the variance of X.

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A First Course in Probability (10th Edition)

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Chapter1: Combinatorial Analysis

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Areas under normal distribution curves can be used calculate probabilities of many random variables in the natural and social sciences. The graph of the Standard Normal Curve, with a mean of 0 and a standard deviation of 1 is given below, and its function is given by 1 f(x) = √2T e 1 The integral of e dx would be used to calculate the probability of an event that occurs √2T -1.5 between -1.5 to 1.5 standard deviations from the mean. (-1.5, 0.13) 1 Unfortunately, √2π -1.5 methods to approximate the values. 1.5 -1.5 1.5 (-1, 0.24) Using Simpson's Rule, (-0.5, 0.35) e dx has no proper closed form antiderivative, so we must use numerical 1.5 -1.5 1-0.5 -0-2 Using the Midpoint Rule with three rectangles of equal width, dx 0 Using the Trapezoidal Rule with six trapezoids of equal width, (0, 0.4) 0.5 Round answers to 4 decimal places when appropriate. (0.5, 0.35) (1, 0.24) 1.5 Ibe 1.5 1.5 [ 13 e-t de = \ е 1.5 e-2 е dx (1.5, 0.13)
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Suppose that the random variable X has the following cumulative distribution function. F(x) = x < 2 4) 2 ≤ x < 3 x > 3 {fc²_. (a) Find P(X> 2.50) (b) Find P(1.16 < X < 2.09) (c) Find the mean of X.