Question

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

Answer #1

Find the standard deviation of the distribution that has the
following probability density function:
f(x)={ 2x, 0<x<1 0, O.W.

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)).

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 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.

1. Let fX(x;μ,σ2) denote the probability density function of a
normally distributed variable X with mean μ and variance σ2.
a. What value of x maximizes this function?
b. What is the maximum value of fX(x;μ,σ2)?

1. Decide if f(x) = 1/2x2dx on the interval [1, 4] is
a probability density function
2. Decide if f(x) = 1/81x3dx on the interval [0, 3]
is a probability density function.
3. Find a value for k such that f(x) = kx on the interval [2, 3]
is a probability density function.
4. Let f(x) = 1 /2 e -x/2 on the interval [0, ∞).
a. Show that f(x) is a probability density function
b. . Find P(0 ≤...

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.

7. For the random variable x with probability density function:
f(x) = {1/2 if 0 < x< 1, x − 1 if 1 ≤ x < 2}
a. (4 points) Find the CDF function. b. (3 points) Find p(x <
1.5). c. (3 points) Find P(X<0.5 or X>1.5)

6. A continuous random variable X has probability density
function
f(x) =
0 if x< 0
x/4 if 0 < or = x< 2
1/2 if 2 < or = x< 3
0 if x> or = 3
(a) Find P(X<1)
(b) Find P(X<2.5)
(c) Find the cumulative distribution function F(x) = P(X< or
= x). Be sure to define the function for all real numbers x. (Hint:
The cdf will involve four pieces, depending on an interval/range
for x....

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