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1. The time to failure X of a component is uniformly distributed on [0, al. Show...
2.27 The time to failure T of a component is assumed to be uniformly distributed over (a, b. The probability density is thus (1)for a<isb b-a Derive the corresponding survivor function R(t) and failure rate function z(). Draw a sketch of z()
The time to failure T of a component is assumed to be uniformly distributed over (a, b]. The probability density is thus for a<t< b Derive the corresponding survivor function R(t) and failure rate function z(t). Draw a sketch of z(t).
Suppose Y is uniformly distributed on (0, 1), and that the conditional distribution of X given that Y -y is uniform on (0, y). Find E[X] and Var(X).
Suppose Y is uniformly distributed on (0, 1), and that the conditional distribution of X given that Y -y is uniform on (0, y). Find E[X] and Var(X).
1. A binomial random variable has the moment generating function, (t) E(etx)II1 E(etX) (pet+1-p)". Show that EX] = np and Var(X) = np(1-p) using that EX] = ψ(0) and E(X2] = ψ"(0). 2. Lex X be uniformly distributed over (a,b). Show that E[xt and Var(X) using the first and second moments of this random variable where the pdf of X is f(x). Note that the nth moment of a continuous random variable is defined as EXj-Γοχ"f(x)dx (b-a)2 exp 2
(5 points) Let X be a Unif(-4, 4) variable, that is, X is Uniformly distributed over the interval (-4,4) Provide answers to the following to two decimal places Part a) Find the MGF of X, evaluated at the point = 1.52. 35.9397 Part b) Let Xi,X2,... , X, be independent Unif(-4,4) variables. Let Find the MGF My(t) of Y. Evaluate the MGF at the point t 0.38 in the case n 5 6.02326 Part c) Find the standard deviation of...
Show all work! Thank you! kxk-1 4.34 Given the pdf for X is f(x)= 10 0<x<1 otherwise determine E[X] and Var[X]. 1 0<x<1 4.35 Given the pdf for X is f(x)=x. determine E[X] and Var[X]. 10 otherwise' Sections 4.5-4.8 A<x<B 4.36 Given a random variable with pdf f(x)= B-A , determine the MGF for this random variable. 10 otherwise so x50 4.37 Given a random variable with pdf f(x)= betx 0<x , determine the MGF for this random variable. '...
Problem 5. Suppose that a uniformly distributed random number X in 0 is found by calling a random number generator. Then, if the call to the RNG pro- duces the value r for X, another random umber Y is computed that is uniformly distributed on 0, . That is, X is uniform on the interval 0,1], and the conditional distribution for Y given X = 1 is uniform on the interval [0.11 a) Give fonmulas for E(Y X) and Var(Y...
Suppose Y is uniformly distributed on (0,1), and that the conditional distribution of X given that Y = y is uniform on (0, y). Find E[X]and Var(X).
Let XU(a, b) be a uniformly distributed random variable. Use the definition of mean and variance to show that: (a) E(X)t (b) Var(x)2