Question: Suppose that a discrete random variable X has probability function f (x) = P(X = x) = 1 5, x RX = {2a,a, 0,

Suppose that a discrete random variable X has probability function f (x) = P(X = x) = 1 5, x ∈ RX = {−2a,−a, 0,

a, 2a}.

(i) Show that, regardless of the value of

a, we have E(X) = 0.

(ii) Calculate Var(X) as a function of

a. What happens with the variance as a increases? Give an intuitive interpretation of this result.

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock blur-text-image
Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock
Step: 3 Unlock

Students Have Also Explored These Related Introduction To Probability Statistics Questions!

Q:

complete all using simple calculations 1 Consider the following two random samples of ten observations which come from the distributions of random variables which assume non-negative integer values...

Q:

QUESTION 1 Let A and B be independent events.Which of the following is always TRUE for these events? A.P(A and B) = P(A) P(B) B.P(A or B) = P(A) + P(B) C.P(A given B) = P(B) D.All of the above are...

Q:

(1) Let X be a discrete random variable with a probability function given by p (x) = c 7 x, for x = 1,. . . , 6, where is a positive real constant. Determine: (a) the value of the constant c. (b) the...

Q:

D Question 8 11 pts I have an unfair coin that shows heads only 25% of the time. We want to play a game, but you don't know whether I am using the unfair coin or a fair one. You suspect I am...

Q:

1-Let X be a discrete random variable with a probability function given byp(x) = c 7 x, para x = 1, . . . , 6 where is one positive real constant. Determine: (a) the value of the constant c. (b) the...

Q:

Solve all the questions well 1 The time taken to process simple home insurance claims has a mean of 20 mins and a standard deviation of 5 mins. Stating clearly any assumptions that you make,...

Q:

10:38 4 .III LTE (E) v / Tests / Test3 Time left 0:59:36 Question 4 Not yet answered Marked out of 1.00 \\V Flag question Two events E and F are independent if P(En F) = P(E) + P(F) Select one: 0...

Q:

DURATION :1 HOUR 15 MINUTES [TOTAL: 35 MARKS] ANSWER ALL QUESTIONS. ALL STEPS MUST BE SHOWN CLEARLY. 1. Suppose that a discrete random variable X has the following cumulative distribution function...

Q:

4-54. Let X be a discrete random variable with probability mass function f (X). If a random variable Y = a+bX, b = 0, then the probability mass function of Y is g(y) = f y a b . Verify this result...

Q:

Hi .. need help with these questions e and f.. Thank you! (e) Suppose that a discrete random variable X is uniform on the interval {-4, -3, -2, -1, 0, 1, 2, 3, 4). Let Y = X . Show that X and Y are...

Q:

Information from Minor Company's income statement for the year ended December 31, 2019 is shown below. Additional information from Minor Company's comparative balance sheet is also shown below....

Q:

Derive the formula for the energy density of radiation inside an enclosed cavity at constant temperature T using classical physics. Show how the classical theory is modified to correctly explain the...

Q:

Which type of audit can be handled entirely by telephone or through the mail? Multiple Choice Correspondence examination Office examination Field examination All of these choices are correct.

Q:

Find the indicated matrices using a calculator. 1/3B 1/2A A = c = C 6-3 4 -5 B = -1 4 -7 2 -6 11 3 -9 D = 12 -6 79-6 -4 0 8

Q:

Find the median for the set of measurements 2, 9, 11, 5, 6, 27.

Q:

For the n = 5 ordered measurements from Example 2.2, the position of the median is 0.5(n+1)=0.5(6) = 3, and the median is the 3rd ordered observation, or m = 6. For the n = 6 ordered measurements...

Q:

2.1 You are given n = 5 measurements: 0, 5, 1, 1, 3. a. Draw a dotplot for the data. (HINT: If two measurements are the same, place one dot above the other.) Guess the approximate "centre." b. Find...

Q:

View Policies Current Attempt in Progress For the year ended December 31, 2022, the job cost sheets of Sunland Company contained the following data. Job Number 7640 Explanation Balance 1/1 Direct...

Q:

Massive Limousines uses activity-based costing for its two models of stretch Hummer limousines: Big and Too Big. There are three activity cost pools related to production, with estimated costs and...

Q:

The Caldwell Herald newspaper reported the following story: Frank Ormsby of Caldwell is the state's newest millionaire. By choosing the six winning numbers on last week's state lottery, Mr. Ormsby...