Question

Question 6) Suppose X is a random variable taking on possible values 0,2,4 with respective probabilities .5, .3, and .2. Y is a random variable independent from X taking on possible values 1,3,5 with respective probabilities .2, .2, and .6. Use R to determine the following.

f) Find the expected value of X*Y. (i.e. X times Y)

g) Find the expected value of 3X - 5Y.

h) Find the variance of 3X - 5Y

i) Find the expected value of Y^{4}

i) Copy your R script for the above into the text box here.

Answer #1

**(f) E(x*y)= 5.32 =
sum(y*p)*sum(x*q)**

**(g) E(3x-5y)
= sum(y*y*p)-sum(y*p)*sum(y*p) = 2.56**

**(h) V(3x-5y) =
5*5*{sum(y*y*p)-sum(y*p)*sum(y*p)}+3*3*{sum(x*x*q)-sum(x*q)*sum(x*q)}
= 85.96**

**and note that "y4 " is meaningless here so i ommited
it.**

Suppose X is a random variable taking on possible values 0,2,4
with respective probabilities .5, .3, and .2. Y is a random
variable independent from X taking on possible values 1,3,5 with
respective probabilities .2, .2, and .6. Use R to determine
the following.
a) Find the expected value of Y.
b) Find the variance of Y.
c) Find the expected value of Y4 .
PLEASE SHOW ANSWER IN R SCRIPT

Question 6) Suppose X is a random variable taking on possible
values 0,2,4 with respective probabilities .5, .3, and .2. Y is a
random variable independent from X taking on possible values 1,3,5
with respective probabilities .2, .2, and .6. Use R to determine
the following.
a) Find the probability P(X*Y = 4)
b) Find the expected value of X.
c) Find the variance of X.
d) Find the expected value of Y.
e) Find the variance of Y.

Question 7) Suppose X is a Normal random variable with with
expected value 31 and standard deviation 3.11. We take a random
sample of size n from the distribution of X. Let X be the sample
mean. Use R to determine the following:
a) Find the probability P(X>32.1):
b) Find the probability P(X >32.1) when n = 4:
c) Find the probability P(X >32.1) when n = 25:
d) What is the probability P(31.8 <X <32.5) when n =
25?...

Problem #3. X is a random variable with an exponential
distribution with rate λ = 7 Thus the pdf of X is f(x) = λ
e−λx for 0 ≤ x where λ = 7.
a) Using the f(x) above and the R integrate function calculate the
expected value of X.
b) Using the f(x) above and the R integrate function calculate the
expected value of X2
c) Using the dexp function and the R integrate command calculate
the expected value...

Problem #3. X is a random variable with an exponential
distribution with rate λ = 7 Thus the pdf of X is f(x) = λ
e−λx
for 0 ≤ x where λ = 7.
PLEASE ANSWER these parts if you can.
f) Calculate the probability that X is at least .3 more
than its expected value.Use the pexp function:
g) Copy your R script for the above into the text box
here.

Question 2) The density of random variable X is f(x) =
15(x2−36)(64−x2) / 3904 for 6 ≤ x ≤ 8 and 0
otherwise. Do computations using the R integrate function.
a) Find the probability that X > 7:
b) Find the probability that 6.5 < X < 7.5:
e) Find the probability that x is within one standard deviation
of its expected value:
f) In the following paste your R script for this problem:

Suppose X is a random variable with with expected value -0.01
and standard deviation σ = 0.04.
Let
X1,
X2, ...
,X81
be a random sample of 81 observations from the distribution of
X.
Let X be the sample mean. Use R to determine the
following:
Copy your R script
b) What is the approximate probability that
X1 +
X2 + ...
+X81 >−0.02?

The expected values, variances and standard Deviatiations for
two random variables X and Y are given in the following table
Variable
expected value
variance
standard deviation
X
20
9
3
Y
35
25
5
Find the expected value and standard deviation of the following
combinations of the variable X and Y. Round to nearest whole
number.
E(X+10) = ,
StDev(X+10) =
E(2X) = ,
StDev(2X) =
E(3X-2) = ,
StDev(3X-2) =
E(3X +4Y) = ,
StDev(3X+4Y) =
E(X-2Y) = ,
StDev(X-2Y) =

Consider the probability distribution of a random variable x. Is
the expected value of the distribution necessarily one of the
possible values of x? Explain and give examples.
WRITE IN TEXT NOT IN IMAGE TEXT SINCE I CANT READ SOME OF THE
TEXT IN IMAGE

Let X be a random variable with a mean of 9 and a variance of
16. Let Y be a random variable with a mean of 10 and a variance of
25. Suppose the population correlation coefficient between random
variables X and Y is -0.4.
a) Find the mean of the random variable W = 3X - 5Y.
b) Find the standard deviation of the random variable Z = X +
Y

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 6 minutes ago

asked 9 minutes ago

asked 10 minutes ago

asked 18 minutes ago

asked 26 minutes ago

asked 30 minutes ago

asked 44 minutes ago

asked 45 minutes ago

asked 54 minutes ago

asked 54 minutes ago

asked 1 hour ago

asked 1 hour ago