Question

The probability desinity function of X is f(x)=ax+b on the interval [0,2] and it is 0 elsewhere. You are given that the median of X is 1.25. Find a and b

Answer #1

a=0.267 & b=0.233

The
r.v. X has the probability density function f (x) = ax + bx2 if 0
< x < 1 and zero otherwise. If E[X] = 0.6, find (a) P[X <
21] and (b) Var(X). (Answers should be in numerical values and not
be as expressions in a and b.)

A random variable X has a probability function f(x) = Ax, 0 ≤ x
≤ 1, 0, otherwise.
a. What is the value of A? (Hint: intigral -inf to inf f(x)dx=
1.)
b. Compute P(0less than x less than 1/3)
c. Compute the cdf. of X.
d. Compute E(X).
e. Compute V(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

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 ≤...

a) The joint probability density function of the random
variables X, Y is given as
f(x,y) =
8xy
if 0≤y≤x≤1 , and 0
elsewhere.
Find the marginal probability density functions.
b) Find the expected values EX and
EY for the density function above
c) find Cov X,Y .

Find the Fourier series of the function f on the given
interval.
f(x) =
0,
−π < x < 0
1,
0 ≤ x < π

given the conditions for a function (f(x))
f '(x) > 0 on (0,3)
• f '(x) < 0 on (3,∞)
• f ''(x) > 0 on (0,2)
• f ''(x) < 0 on (−∞,0) ∪ (2,∞)
how would the graph f(x) look like?

Suppose that ff is a Riemann integrable function on [0,2][0,2]
and that ∫20f(x)dx=5∫02f(x)dx=5. Suppose further that AA is a
function such that if 0≤a≤20≤a≤2 then the average value of ff on
the interval [0,a][0,a] is given by A(a)A(a). Find a formula for
the average value of ff on [a,2][a,2] using AA.

Consider the given function and the given interval. f(x) = 5 x ,
[0, 4] (a) Find the average value fave of f on the given interval.
(b) Find c such that fave = f(c). (Round your answer to three
decimal places.) c =

The probability distribution function for the random variable X,
the lead content in a liter of gasoline is: (a) Prove that f(x) IS
a probability distribution function (b) Find the expected value of
lead content in a liter of gasoline (c) Find the standard deviation
of the lead content in a liter of gasoline (d) Find the equation
for the cumulative distribution function of X f(x) = 12.5x – 1.25,
0.10 < x < 0.50 0, elsewhere

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