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- Assume that the probability that an airplane engine will fail during a torture test is 12and that the aircraft in question has 4 engines. Construct a sample space for the torture test. Use S for survive and F for fail.If a binomial experiment has probability p success, then the probability of failure is ____________________. The probability of getting exactly r successes in n trials of this experiment is C(_________, _________)p (1p)Let f(x, y) = x + y for 0 < x < 1 and 0 < y < 1 The Conditional Variance of Y when X = ; is
- Suppose that the random variables X and Y are independent with Var(X)=8 and Var(Y)=6. Calculate Var(5X−7Y+17)7) For the continuous probability distribution f(x) = kx³e-x Where x 20, find mean.Each front tire on a particular type of vehicle is supposed to be filled to a pressure of 24 psi. Suppose the actual air pressure in each tire is a random variable-X for the right tire and Y for the left tire, with joint pdf will be f(x, y) = K (x² + y²) if 20 ≤ x ≤ 30, 20 ≤ y ≤ 30 Are X and Y independent random variables? In order to answer this question, you need to find the value for K first. X and Y are not independent. X and Y are independent. cannot decide none of the other option is correct
- 25. Show that if X is a random variable and g(.) is a Borel measurable function, then Y = g(X) is a random variable.Each front tire on a particular type of vehicle is supposed to be filled to a pressure of 26 psi. Suppose the actual air pressure in each tire is a random variable, X for the right tire and Y for the left tire, with joint pdf F(x, y) = { K (x² + y²) 20 ≤ ≤ 30, 20 ≤ y ≤ 30 otherwise (a) What is the value of K? (Enter your answer as a fraction.) K= (b) What is the probability that both tires are underfilled? (Round your answer to four decimal places.) (c) What is the probability that the difference in air pressure between the two tires is at most 2 psi? (Round your answer to four decimal places.) (d) Determine the (marginal) distribution of air pressure in the right tire alone. for 20≤x≤ 30 (e) Are X and Y independent rv's? Oves, f(x, y) = fx(z) - fy (y), so X and Y are independent. Oves, f(x, y) + fx(z) - fy(y), so X and Y are independent. ONO, f(x, y) = fx(2) - fy(y), so X and Y are not independent. ONO, f(z,y) #fx(z) - fy(y), so X and Y are not independent.3. Let Y be the number of speeding tickets a YSU student got last year. Suppose Y has probabilitymass function (PMF)y 0 1 2 3fY (y) 0.12 0.13 0.33 0.42(a) What is the probability a YSU student got exactly one ticket?(b) What is the probability a YSU student got at least one ticket?(c) Compute µY , the mean of Y .(d) Find the variance and standard deviation of Y .(e) What is the probability that Y exceeds its mean value?
- For what values of k canf(x) = (1 − k)kx serve as the values of the probability distribution of arandom variable with the countably infinite range x =0, 1, 2, ...?Z is the present-value random variable for a whole life insurance of b payable at the moment of death of (x). You are given: (i) (ii) 8 = 0.05 (iii) The net single premium for this insurance is equal to Var(Z). Calculate b. x+t = 0.01 t≥0 (A) 1.36 (B) 1.68 (C) 2.00 (D) 2.32 (E) 2.64Let X be a random variable with E(X)= 1 and E[X(X-1)]=4,then evaluate Var(2-3X). (a)28 (b)42 (c) 26 (d) 36
