Question

Let N be a positive integer random variable with PMF of the form

pN(n)=1/2⋅n⋅2^(−n),n=1,2,…. |

Once we see the numerical value of N, we then draw a random variable K whose (conditional) PMF is uniform on the set {1,2,…,2n}.

Find the marginal PMF pK(k) as a function of k. For simplicity,
provide the answer **only for the case when** k
**is an even number**. (The formula for when k is odd
would be slightly different, and you do not need to provide
it).

For k=2,4,6,…:

pK(k)=

Answer #1

Let N be a positive integer random variable with PMF of the form
pN(n)=12⋅n⋅2−n,n=1,2,…. Once we see the numerical value of N , we
then draw a random variable K whose (conditional) PMF is uniform on
the set {1,2,…,2n} . 1. Find joint PMF pN,K(n,k) For n=1,2,… and
k=1,2,…,2n 2. Find the marginal PMF pK(k) as a function of k . For
simplicity, provide the answer only for the case when k is an even
number. For k=2,4,6,… 3. Let...

For all problems on this page, use the following setup:
Let N be a positive integer random variable with PMF of the
form
pN(n)=1/2⋅n⋅2^(−n),n=1,2,….
Once we see the numerical value of N, we then draw a random
variable K whose (conditional) PMF is uniform on the set
{1,2,…,2n}.
Write down an expression for the joint PMF pN,K(n,k).
For n=1,2,… and k=1,2,…,2n:
pN,K(n,k)=

Let K be a random variable that takes, with equal probability
1/(2n+1), the integer values in the interval [-n,n].
Find the PMF of the random variable Y = In X. Where X = a^[k]. and
a is a positive number, let n = 7 and a = 2. Then what is E[Y
]?

1.A fair die is rolled once, and the number score is noted.
Let the random variable X be twice this score. Define the variable
Y to be zero if an odd number appears and X otherwise. By finding
the probability mass function in each case, find the expectation of
the following random variables:
Please answer to 3 decimal places.
Part a)X
Part b)Y
Part c)X+Y
Part d)XY
——-
2.To examine the effectiveness of its four annual advertising
promotions, a mail...

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