continuous random variable with probability density function given o re-x/100 f(x) = 0. X < 0 What is the probability that (a) a computer will function between 50 and 150 hours before breaking down? (b) it will function for fewer than 100 hours?
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- Q5 Let the density function of a continuous random variable X if given by (k x(2 – x) 0What is the probability density with given random variable value? f(x₁) = 1 Data are distributed according to a probability density function f(x) standardized random variable and the probability density with random variable value x₁ = -0.7100 ? 4.77√(2T) What is the standardized random variable value? 21 = 1 What is the standardized pdf with given random variable value? Y(2₁) = 1 What is the cdf with given random variable value? F(x₁) = 1 % What is the standardized cdf with given random variable value? $(21) = 1 % Do not leave any fields blank. If you don't know the answer, insert 1 for example. Insert only 3 most significant digits of your answer without rounding. Constant Value Unit 0.1900 4.7700 fl o Quantity mean standard deviation random variable random variable value Symbol fl o x x1 probability density function f(x) cumulative distribution function F(x) probability density with given random variable value f(x₁) cdf with given random variable value F(x₁) standardized random…(Device lifetime) A satellite orbiting the Earth contains a device whose lifetime X (in years) has the exponential distribution with parameter λ = 0.5. (a) Show how the cumulative distribution function F(t) is obtained by integrating the density. (b) Directly from the CDF, calculate the probabilities of the events A = {X ≤ 1}, B = {X > 5}, and C = {5 < X ≤ 6}. Give the results with at least 6 decimals. Explain in words what this events are. (c) From the numerical results in (b), and using the definition of conditional probability, calculate P(C|B). Compare to P(A) and explain. = (d) Consider a very short interval of h 0.01 years. If the device has lasted to a certain point in time, what is the probability that it breaks during the next 0.01 years? Compare your numerical result to the value of Xh, and explain why A is called the rate parameter.The probability density function of random variable X is given by 20 30 x 30 x<20 x2 F (x) = -+4 20SEE MORE QUESTIONSRecommended textbooks for youA First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON
A First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON