Question

i) A random variable X has a binomial distribution with mean 6 and variance 3.6: Find P(X = 4).

ii) Let X equal the larger outcome when a pair of four-sided dice is rolled. The pmf of X is

f(x) = (2x - 1/ 16) ; x = 1; 2; 3; 4.

Find the mean, variance and standard deviation of X.

iii) Let μ and σ^2 denote the mean and variance of the random variable able X. Determine E [(X - μ/σ ] and E{ [(X -μ)/σ ]^2}

Answer #1

If x is a binomial random variable, compute the mean,
the standard deviation, and the variance for each of the following
cases:
(a)
n=4,p=0.7
μ=
σ2=
σ=
(b)
n=3,p=0.7
μ=
σ2=
σ=
(c)
n=5,p=0.4
μ=
σ2=
σ=
(d)
n=5,p=0.8
μ=
σ2=
σ=

Let X be a Gaussian random variable with mean
μ and variance σ^2. Compute the following
moments:
Remember that we use the terms Gaussian random
variable and normal random variable
interchangeably.
(Enter your answers in terms of μ and σ.)
E[X^2]=
E[X^3]=
E[X^4]=
Var(X^2)=
Please give the detail process of proof.

1) Suppose a random variable, x, arises from a binomial
experiment. Suppose n = 6, and p = 0.11.
Write the probability distribution. Round to six decimal places,
if necessary.
x
P(x)
0
1
2
3
4
5
6
Find the mean.
μ =
Find the variance.
σ2 =
Find the standard deviation. Round to four decimal places, if
necessary.
σ =
2) Suppose a random variable, x, arises from a binomial
experiment. Suppose n = 10, and p =...

Let X be a binomial random variable with n = 10 and p = 0.2.
Find the following values. (Round your answers to three decimal
places.) (a) P(X = 4) (b) P(X ≥ 4) (c) P(X > 4) (d) P(X ≤ 4) (e)
μ = np μ = 2.00 (correct) (f) σ = npq σ = 1.265 (correct)

Let
X be a random variable with mean μ and variance σ^2. Define
Y=(X-μ)/σ. What is the variance of Y?

Two identical fair 6-sided dice are rolled
simultaneously. Each die that shows a number less than or equal to
4 is rolled once again. Let X be the number of dice that show a
number less than or equal to 4 on the first roll, and let Y be the
total number of dice that show a number greater than 4 at the
end.
(a) Find the joint PMF of X and Y . (Show your final
answer in a...

(A random variable ? has a binomial distribution with
mean 2.79 and variance 1.9251)
please find this ?(?≤3).

Suppose that a random variable X has a binomial distribution
with n=2, p=0.5. Find the mean and variance of Y =
X2

Find the mean, μ, and standard deviation, σ, for a binomial
random variable X. (Round all answers for σ to three decimal
places.)
(a) n = 45, p = .50.
μ =
σ =
(b) n = 1, p = 0.25.
μ =
σ =
(c) n = 100, p = 0.75.
μ =
σ =
(d) n = 30, p = .01.
μ =
σ =

Roll a die and let its outcome be the random variable X. Let Y
be the random variable of “sum of X many dice rolled”. So, if X is
3, then we roll 3 dice and add the faces together to find Y .
(a) Are X and Y independent? Explain.
(b) Compute E[Y]

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