Question

Find E(X),Var(X),σ(X) if a random variable x is given by its density function f(x), such that f(x)=0, if x≤0 f(x)=2x5, if 0<x≤1 f(x)=0, if x>1

Answer #1

**Answer:**

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that:**

Find E(X),Var(X),σ(X) if a random variable x is given by its density function f(x), such that f(x)=0, if x≤0 f(x)=2x^5, if 0<x≤1 f(x)=0, if x>1

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)

Find the expected value
E(X),
the variance
Var(X)
and the standard deviation
σ(X)
for the density function. (Round your answers to four decimal
places.)
f(x) = ex
on
[0, ln 2]
E(X)
=
Var(X)
=
σ(X)
=

Find the expected value E(X), the variance Var(X) and the
standard deviation σ(X) for the density function. (Round your
answers to four decimal places.) f(x) = ex on [0, ln 2] E(X) =
Var(X) = σ(X) =

Find the expected value E(X), the variance Var(X) and the
standard deviation σ(X) for the density function. (Round your
answers to four decimal places.) f(x) = e^x on [0, ln 2]?

The random variable X has a probability density function f(x) =
e^(−x) for x > 0. If a > 0 and A is the event that X > a,
find f XIA (xlx > a), i.e. the density of the conditional
distribution of X given that X > a.

7. Suppose that random variables X and Y have a joint density
function given by: f(x, y) = ? + ? 0 ≤ ?≤ 1, 0 ≤ ? ≤ 1
(a) Find the density functions of X and Y, f(x) and f(y).
(b) Find E[X] and Var(Y).

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.

Probability density function of the continuous random variable X
is given by f(x) = ( ce −1 8 x for x ≥ 0 0 elsewhere
(a) Determine the value of the constant c.
(b) Find P(X ≤ 36).
(c) Determine k such that P(X > k) = e −2 .

1. f is a probability density function for the random
variable X defined on the given interval. Find the
indicated probabilities.
f(x) = 1/36(9 − x2); [−3, 3]
(a) P(−1 ≤ X ≤ 1)(9 −
x2); [−3, 3]
(b) P(X ≤ 0)
(c) P(X > −1)
(d) P(X = 0)
2. Find the value of the constant k such that the
function is a probability density function on the indicated
interval.
f(x) = kx2; [0,
3]
k=

A random variable X has probability density function f(x)
defined by f(x) = cx−6 if x > 1, and f(x) = 0, otherwise.
a. Find the constant c.
b. Calculate E(X) and Var(X).
c. Now assume Z1, Z2, Z3, Z4 are independent RVs whose
distribution is identical to that of X. Compute E[(Z1 +Z2 +Z3
+Z4)/4] and Var[(Z1 +Z2 +Z3 +Z4)/4].
d. Let Y = 1/X, using the formula to find the pdf of Y.

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