Exercise 06.27 Algo (Exponential Probability Distribution) Consider the following exponential probability density function. a. Which of the following is the formula for P(x ≤ xo)? 1 P(x ≤ xo) = e 2 P(x≤o)=1-e -79 3 P(x≤0)=1-e0 - Select your answer V b. Find P(x <2) (to 4 decimals). c. Find P(x ≥ 4) (to 4 decimals). d. Find P(x ≤5) (to 4 decimals). e. Find P(2≤x≤5) (to 4 decimals). f(x) = 1 e- for 20
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- 1. The lifetime, X, of a CPU in the Edsel computer, measured in months, has the following probability density function: f(x)= 338 x3 for x ≥ 13 and 0 otherwise.a) What is the probability that an Edsel CPU lasts at least two years? b) What is the probability that X < 15? c) What is the probability that 13< X < 20? d) What is the expected value of X (E(X))? e) What is the expected value of X - 7? f) What is the expected value of 3X? g) What is the expected value of 1 X ? h) What is the probability that X is less than its expected value? i) What is the expected value of X ? j) What is the 50th percentile of X? k) What is the probability that X is within 1 standard deviation of its expected value? l) What is the probability that X = 15? m) Add any comments into the text box here.The lifetime, X, of a CPU in the Edsel computer, measured in months, has the following probability density function: f(x)= 338 x3 for x ≥ 13 and 0 otherwise. d) What is the expected value of X (E(X))? e) What is the expected value of X - 7? f) What is the expected value of 3X?Verify that p(x) = 3x−4 is a probability density function on [1,∞) and calculate its mean value.
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- The table below shows a probability density function for a discrete random variable X. What is the probability that X is 0, 3, or 5? Provide the final answer as a fraction. x P(X = x) 0 1/20 1 1/10 2 1/10 3 1/4 4 1/10 5 2/5The table below shows a probability density function for a discrete random variable X, the number of technological devices per household in a small city. What is the probability that X is 0, 2, or 3? Provide the final answer as a fraction. x P(X = x) 0 3/20 1 1/20 2 1/4 3 3/10 4 1/5 5 1/20Q2 - A corporation produces packages of paper clips. The number of clips per package varies, as indicated below for a sample of 20 packages. 52 50 51 53 52 49 50 47 48 51 53 50 48 51 53 50 52 49 47 51 Create a probability density function. What is the probability that a randomly chosen package contains between 47 and 52 clips (inclusive) per package? Please specify your answer in decimal terms and round your answer to the nearest hundredth (e.g., enter 12 percent as 0.12).