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19 a) Find the probability that X > 0.5 0.4753 b) Find the probability that 0.3 < X < 0.63 0.3423 c) Find the expected value of x 0.4825 d) Find the variance of X 0.0806 e) Find the standard deviation of X 0.2838 f) Find the probability that X is within 0.5 standard deviations of its expected value

19 a) Find the probability that X > 0.5 0.4753 b) Find the probability that 0.3 < X < 0.63 0.3423 c) Find the expected value of x 0.4825 d) Find the variance of X 0.0806 e) Find the standard deviation of X 0.2838 f) Find the probability that X is within 0.5 standard deviations of its expected value

College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter8: Sequences, Series, And Probability
Section8.7: Probability
Problem 39E: Assume that the probability that an airplane engine will fail during a torture test is 12and that...
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The probability density function of random variable X is f(x) = a) Find the probability that X > 0.5 0.4753 b) Find the probability that 0.3 < X < 0.63 0.3423 c) Find the expected value of X 0.4825 d) Find the variance of X 0.0806 ✔ e) Find the standard deviation of X 0.2838 5.X for 0 ≤ x ≤ 1 and 0 otherwise. Do computations using the R integrate function. 19 f) Find the probability that X is within 0.5 standard deviations of its expected value g) In the following paste your R script for this problem b = integrate(h.lower=0,upper-1)$value #var(x) var = b-(a)^2 print(var) #standard deviation sqrt(var)
Transcribed Image Text:The probability density function of random variable X is f(x) = a) Find the probability that X > 0.5 0.4753 b) Find the probability that 0.3 < X < 0.63 0.3423 c) Find the expected value of X 0.4825 d) Find the variance of X 0.0806 ✔ e) Find the standard deviation of X 0.2838 5.X for 0 ≤ x ≤ 1 and 0 otherwise. Do computations using the R integrate function. 19 f) Find the probability that X is within 0.5 standard deviations of its expected value g) In the following paste your R script for this problem b = integrate(h.lower=0,upper-1)$value #var(x) var = b-(a)^2 print(var) #standard deviation sqrt(var)
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