Question

Let F(x) = 1 − e −2x for x > 0 and F(x) = 0 for x ≤ 0. Is F(x) a distribution function? Explain your answer. If it is a distribution function, find its density function.

Answer #1

so, PDF ,f(x)=2*e^-2x for x>0 and 0 for x<0

Let the probability density function of the random variable X be
f(x) = { e ^2x if x ≤ 0 ;1 /x ^2 if x ≥ 2 ; 0 otherwise}
Find the cumulative distribution function (cdf) of X.

Let X have the distribution that has the following probability
density function:
f(x)={2x,0<x<1
{0, Otherwise
Find the probability that X>0.5.
Why is the probability 0.75 and not 0.5?

Let the probability density of X be given by f(x) = c(4x - 2x^2
), 0 < x < 2; 0, otherwise. a) What is the value of c? b)
What is the cumulative distribution function of X?
c) Find P(X<1|(1/2)<X<(3/2)).

a) let X follow the probability density function f(x):=e^(-x) if
x>0, if Y is an independent random variable following an
identical distribution f(x):=e^(-x) if x>0, calculate the moment
generating function of 2X+3Y
b) If X follows a bernoulli(0.5), and Y follows a
Binomial(3,0.5), and if X and Y are independent, calculate the
probability P(X+Y=3) and P(X=0|X+Y=3)

let the density function of x be f(x) = e^−x, x>0, find of
the density function of Z = e^-x

1. Find k so that f(x) is a probability density function. k=
___________
f(x)= { 7k/x^5 0 1 < x < infinity elsewhere
2. The probability density function of X is f(x).
F(1.5)=___________
f(x) = {(1/2)x^3 - (3/8)x^2 0 0 < x < 2
elsewhere
3. F(x) is the distribution function of X. Find the probability
density function of X. Give your answer as a piecewise
function.
F(x) = {3x^2 - 2x^3 0 0<x<1 elsewhere

Let f(x, y) = c/x, 0 < y < x < 1 be the joint density
function of X and Y .
a) What is the value of c?
a) 1 b) 2 c) 1/2 d) 2/3 e) 3/2
b)what is the marginal probability density function of X?
a) x/2 b)1 c)1/x d)x e)2x
c)what is the marginal probability density function of Y ?
a) ln y b)−ln y c)1 d)y e)y2
d)what is E[X]?
a)1 b)2 c)4 d)1/2 e)1/4

How to find the mean of the probability density:
f(x) = e^-2x for -.441<x<.440, and 0 elsewhere.

find μ and σ2 for the probability density.
For distribution function F(X):
F(x)=x^2/2 when 0<x<1
F(x)=2x-x^2/2-1 when 1<=x<2
F(x)=1 when x>=2
1.P(X>1.8) = 0.02
2.P(0.4<=X<=1.6) = 0.84

The density function of random variable X is given by f(x) = 1/4
, if 0
Find P(x>2)
Find the expected value of X, E(X).
Find variance of X, Var(X).
Let F(X) be cumulative distribution function of X. Find
F(3/2)

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