Given the cumulative distribution, x <7 1 F(x) 1, 7 5xs14 0, 1, X> 14 Determine...
The cumulative distribution function of the random variable X is given by F(x) = 1-e-r' (z > 0). Evaluate a) P(X > 2) b) P(l < X < 3 c) P(-1 〈 X <-3). d) P(-1< X <3)
Problem 2 If the cumulative distribution function of X is given by o F(b) = b<0 0<b<1 1<b<2 2<b<3 3<b<3.5 b> 3.5 1 calculate the probability mass function of X.
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2.5.9. The random variable X has a cumulative distribution function 0, forx<0 F(x) for x > 0. for x > , 1+x2" · Find the probability density function of X.
9. The distribution function of a random variable X is given by 0, for r<-1, F(x) = { 271 -1<x<1, 1, 2 > 1. Find (a) P(Z < X < }); (b) P(1<x< 2).
1 A continuous random variable has its cumulative distribution function of the form: 0 2<-1 F() = k(x+1) -1<x<0 1 2 > 0 Which of the following is the pdf for this distribution? 0 2-1 of() = {2.(2+1) -1 <o<0 2 > 0 0 x<-1 Of(0) = { 1.(2+1) -1 <<<0 0 2 > 0 1 <-1 of(x) = { $.1.(2+1) -1 <<<0 20 0 <-1 of(x) = { 2. (+1) -1<x<0 0 2 > 0 None of the above....
dx Determine x= f(t) for (t? +4t) 4x + 4,t> 0; f(1) = 3. dt For (1? + 4t) dx dt = 4x +4, x= f(t) =
Q1. Assume that X is a continuous and nonnegative random variable with the cumulative distribution function F and density f. Let b>0. (a) Write the forinula for E(X b)+1. (b) Apply the general formula from (a) to exponential distribution with parameter λ > 0.
-3x > 0 An exponential distribution is given by f(x) zero, x <0 Find the distribution of the random variable Y X2
Sketch the graph of a function f having the given characteristics. f(3) = f(9) = 0 f'(6) = f'(8) = 0 f'(x) > 0 for x < 6 f'(x) > 0 for 6 < x < 8 f'(x) < 0 for x > 8 f"(x) < 0 for x < 6 or x > 7 f"(x) > 0 for 6 < x < 7
Suppose f is continuous, f(0)=0, f(2)=2, f'(x)>0 and f (x) dx = 1. Find the value of the integral fro f-?(x) dx =?