Question

Provide an example of a probability distribution of discrete random variable, Y, that takes any 4 different integer values between 1 and 20 inclusive; and present the values of Y and their corresponding (non-zero) probabilities in a probability distribution table.

Calculate:

a) E(Y)

b) E(Y2 ) and

c) var(Y).

d) Give examples of values of ? and ? , both non-zero, for a binomial random variable X. Use either the binomial probability formula or the binomial probability cumulative distribution tables provided in class calculate:

a) ?(? = ?0) where ?0 is an integer of your own choice satisfying 0 < ?0 < ?.

b) ?(? > ?0)

e) Suggest any value, ?0, of the standard normal probability distribution (correct to two decimal places), satisfying 1.10 < ?0 < 2.5 and then calculate:

a) P(Z> −?0) and b) P (Z< 0.8?0)

i want the answer of part e as well please solve it too because last time i posted this question that person didnt solve part e for me

Answer #1

A Poisson random variable is a variable X that takes on the
integer values 0 , 1 , 2 , … with a probability mass function given
by p ( i ) = P { X = i } = e − λ λ i i ! for i = 0 , 1 , 2 … ,
where the parameter λ > 0 .
A)Show that ∑ i p ( i ) = 1.
B) Show that the Poisson random...

True or False?
19. In a binomial distribution the random variable X is
discrete.
20. The standard deviation and mean are the same for the
standard normal distribution.
21. In a statistical study, the random variable X = 1, if the
house is colonial and X = 0 if the house is not colonial, then it
can be stated that the random variable is continuous. 22. For a
continuous distribution, P(X ≤ 10) is the same as P(X<10).
23. For...

Suppose X is a discrete random variable that takes on integer
values between 1 and 10, with variance Var(X) = 6. Suppose that you
define a new random variable Y by observing the output of X and
adding 3 to that number. What is the variance of Y? Suppose then
you define a new random variable Z by observing the output of X and
multiplying that by -4. What is the variance of Z?

For a discrete random variable, the probability of the random
variable takes a value within a very small interval must be
A.
zero.
B.
very small.
C.
close to 1.
D.
none of the above.
QUESTION 10
The area under the density function in a certain interval of a
continuous random variable represents
A.
randomness.
B.
the area of one rectangle.
C.
the probability of the interval.
D.
none of the above.
QUESTION 11
For any random variable, X, E(X)...

Suppose that the random variable X has the following cumulative
probability distribution
X: 0 1. 2. 3. 4
F(X): 0.1 0.29. 0.49. 0.8. 1.0
Part 1: Find P open parentheses 1 less or equal than
x less or equal than 2 close parentheses
Part 2: Determine the density function f(x).
Part 3: Find E(X).
Part 4: Find Var(X).
Part 5: Suppose Y = 2X - 3, for all of X, determine
E(Y) and Var(Y)

Analyze the scenario and complete the following:
Complete the discrete probability distribution for the given
variable.
Calculate the expected value and variance of the discrete
probability distribution.
The value of a ticket in a lottery, in which 2,000 tickets are
sold, with 1 grand prize of $2,500, 10 first prizes of $450, 20
second prizes of $125, and 55 third prizes of $40.
i.
xx
0
40
125
450
2,500
P(x)P(x)
Round probabilities to 4 decimal places
ii.
E(X)E(X) =...

The random variable W = X – 3Y + Z + 2 where X, Y and Z are
three independent Normal random variables, with E[X]=E[Y]=E[Z]=2
and Var[X]=9,Var[Y]=1,Var[Z]=3.
The pdf of W is:
Uniform
Poisson
Binomial
Normal
None of the other pdfs.

__________ For a continuous random variable x, the area
under the probability distribution curve between any two x-values
is always _____.
Greater than 1 B) less than
zero C) equal to 1 D) in the
range zero to 1, inclusive
_________For a continuous random variable x, the total
area under the probability distribution curve of x is always
______?
Less
than1 B)
greater than
1
C) equal to
1
D) 0.5
___________ The probability that a continuous random
variable x...

Let X be a discrete random variable that takes on the values −1,
0, and 1. If E (X) = 1/2 and Var(X) = 7/16, what is the probability
mass function of X?

3. (10pts) Let Y be a continuous random variable having a gamma
probability distribution with expected value 3/2 and variance 3/4.
If you run an experiment that generates one-hundred values of Y ,
how many of these values would you expect to find in the interval
[1, 5/2]?
4. (10pts) Let Y be a continuous random variable with density
function f(y) = 1 2 e −|y| , −∞ < y < ∞ 0, elsewhere (a) Find
the moment-generating function of...

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