Let X denote the amount of time a book on two-hour reserve is actually checked out, and suppose the cumulative distribution function is given as follows: F(x)= 16 Osx<4 x24 use the cumulative distribution function (cdf) to obtain P(X s 2) . Leave your answer in two decimal pla
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- Let X be the number of microorganisms in a proliferation culture whose Function of Cumulative Distribution (fda) is given by: F(x) = 1 − e−λx, for x > 0. What is the value of λ such that P(X ≥ 10.14) = 0.8Let X ∼ Unif(0, 2) and Y ∼ Bi(2, 0.5). If Z is a mixture of X and Ywith equal weights, graph the cumulative distribution function of Z, andfind Var(Z).Given the Cumulative Distribution Function(C.D.F) F ( x ) = { 0 , x < − 2 (x + 3)/5 , − 2 ≤ x < 1.5 1 , 1.5 ≤ x Compute P(x>0)
- The time for the first widget to be manufactured each morning is random between 1 and 3 seconds with a pdf of f(x)=1/162(x-3)^2(x+6) for 0 < x < 6What is the cumulative distribution function, F(x)? What is the probability of a widget being made earlier than 4 s?Answer to four decimal places What is the probability of a widget being made later than 1.3 s?Answer to four decimal placesIf F(x1, x2, x3) is the value of the joint distribution function of X1, X2, and X3 at (x1, x2, x3), show that the joint marginal distribution function of X1 and X3 is given by M(x1, x3) = F(x1, q, x3) for −q < x1 < q, −q < x3 < q and that the marginal distribution function of X1 is given by G(x1) = F(x1, q, q) for −q < x1 < q With reference to Example 19, use these results to find (a) the joint marginal distribution function of X1 and X3; (b) the marginal distribution function of X1.Let X be distributed as an exponential with a mean of 1.5. find: a) P(X = 0.16) b) P(X < 0.64) c) P(X > 0.372) d) P(-0.21 < X < 0.70) repeat but let X be uniform on 0 to 1
- Suppose that the probability density function of x is fx=3x2, 0<x<1 0, elsewhere Determine p(x < (1/3)), p((1/3) ≤ x < (2/3)), and p(x ≥ (2/3)) Determine the cumulative distribution function of x.The time, X, to infection for Eagle Flu in minutes, after coming into contact with the virus has cumulative distribution F with the following definition:F(x) = 0 for x < 1 and F(x)= (3/2)-(3/2x) for 0 ≤ x ≤ 3 a) What is the probability density function for X for 1 ≤ x ≤ 3? f(x) = .5 f(x) = (3/4x^2) f(x) =(3/2x^2) f(x) = (3/2)-(3/2x) f(x) = (3x/2x^3) b) What is the probability that X > 2? c) What is the probability X < 2 ? d) What is the probability that X > 2.5? e) What is the probability that X > 3? f) What is the probability that X > 2.5 given the X > 2? g) Calculate the 60th percentile of X. h) What is the expected value of X? i) What is the expected value of X2 j) What is the variance of X? k) What is the probability that X is more than 0.1 above its expected value?LetX1,X2,...,Xn be a sequence of independent and identically distributed random variables having the Exponential(λ) distribution,λ >0, fXi(x) ={λe−λx, x >0 0, otherwise Define the random variable Y=X1+X2+···+Xn. Find E(Y),Var(Y)and the moment generating function ofY.
- Let the random variable X be the portion of a flood insurance claim for flooding damage to a house. The probability density of X has the form f(x)= c(3x2 - 8x - 5) for 0 < x < 1. What is the value of the constant c? What is the cumulative distribution function of X?Verify that the following function is cumulative distribution function, and determine the probability mass function and the requested probabilities. F(x) ={ 0, X < 1 0.5, 1 ≤ x < 3 1, 3 < ? } (a)P(X≤3) (b)P(X ≤2) (c)P(1≤X≤2) (d)P(X>2)Let X = the time between two successive arrivals at the drive-up window of a local bank. If X has an exponential distribution with λ = 1 Compute P(X≤4) and P(2≤X≤5)