Question

If Z is a standard normal random variable and Y = Z^2 . Determine the probability density function fY (y).

Answer #1

TOPIC:Transformation of random variables.

Let X be a normal random variable with ?=−10 and ?=2. Let Z be a
standard normal random variable. Draw density plots for both random
variables on the same graph. You will want an x-axis that goes from
around -20 to around 5. Your y-axis will start at zero and will
need go high enough to cover the highest density. Recall that the
density of a normal random variable at the point ? with mean ? and
standard deviation ?...

Let z be a random variable with a standard normal distribution.
Find the indicated probability. (Round your answer to four decimal
places.) P(z ? ?0.25)
Let z be a random variable with a standard normal distribution.
Find the indicated probability. (Round your answer to four decimal
places.) P(z ? 1.24)
Let z be a random variable with a standard normal distribution.
Find the indicated probability. (Enter your answer to four decimal
places.) P(?2.20 ? z ? 1.08)

Let Z be a standard normal random variable and Y = a +bZ^2+cZ^3
where a, b, c are constants. Compute the correlation p(Y,Z)

Let X be a continuous random variable with a probability density function
fX (x) = 2xI (0,1) (x) and let it be the function´
Y (x) = e^−x
a. Find the expression for the probability density function fY (y).
b. Find the domain of the probability density function fY (y).

A: Let z be a random variable with a standard normal
distribution. Find the indicated probability. (Round your answer to
four decimal places.)
P(z ≤ 1.11) =
B: Let z be a random variable with a standard normal
distribution. Find the indicated probability. (Round your answer to
four decimal places.)
P(z ≥ −1.24) =
C: Let z be a random variable with a standard normal
distribution. Find the indicated probability. (Round your answer to
four decimal places.)
P(−1.78 ≤ z...

If a random variable X follows a standard normal model N(0, 1),
find the
density of X^2
For two independent standard normal random variables X and Y,
find
the density of X^2+Y^2
For three independent standard normal random variables X, Y and
Z,
find the density of X^2+Y^2+Z^2
If a random variable X follows a normal N(μ,σ^2), and a
random variable
Y follows a χ2 (Chi-Square) model with degree of freedom k, assume that X
and Y are
independent,
4.1)...

Let X be a random variable with probability density function
f(x) = {3/10x(3-x) if 0<=x<=2
.........{0 otherwise
a) Find the standard deviation of X to four decimal
places.
b) Find the mean of X to four decimal places.
c) Let y=x2 find the probability density function
fy of Y.

Let z be a random variable with a standard normal
distribution. Find the indicated probability. (Round your answer to
four decimal places.)
P(−0.53 ≤ z ≤ 2.04) =

Let Y be a random variable with a given probability density
function by f (y) = y + ay ^ 2, with y E [0; 1] and a E [0; 2].
Determine: The value of a.
The Y distribution function.
The value of P (0,5 < Y < 1)

a) Let Z be a standart normal RV(random
variable) and If Y = Z^2 for all Z, what is the PDF and mean of Y
?
b) If Y = Z^2 for Z>0 and Y=0 for other
regitions, Calculate PDF of Y and P(Y=0).
c) Calculate P(Y<1) by using table for
both a and b options above.

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