Question: Let X be a random variable with pdf f(x) = kx2 where 0 < x < 1. (a) Find k. (b) Find E(X) and Var

Let X be a random variable with pdf f(x) = kx2 where 0 < x < 1.
(a) Find k.
(b) Find E(X) and Var (X).
(c) Find MX (t). Using the mgf, find E(X).

Step by Step Solution

★★★★★

3.46 Rating (166 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

a b c 1 ... View full answer

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

Document Format (1 attachment)

Word file Icon

610-M-C-P-T (208).docx

120 KBs Word File

Students Have Also Explored These Related Statistics Questions!

Q:

Let X be a random variable with pdf pX (k) = 1/n, for k = 0, 1, 2, . . . , n 1 and 0 otherwise. Show that MX(t) = 1ent/n(1 et).

Q:

Let X be a random variable with mean and variance 2, and let X1, X2,., Xn be a random sample of a continuous random variable with cumulative distribution function F(x). Find E[F(X(n))] and E[F(X(1))].

Q:

Let X be a random variable with E(X) = μ and V (X) = σ2. Show that the function f(x) defined by

Q:

GIVE TYPED WRITING SO I CAN UNDERSTAND CLEARLY. IF YOU CANNOT TYPE,PLEASE PROVIDE NEAT AND CLEAR HANDWRITING.DO NOT GIVE BLUR AND CLUMSY WRITING.IT IS HARD FOR ME TO UNDERSTAND. Kindly give accurate...

Q:

2. Let X be a random variable with PDF M) = SWIG15W, where o: > 0 and A > 0. (a) Find 0. (b) Identify the conditional distribution of X given X > 0. ) ) (0 Compute the nth moment of X. ((1 Obtain the...

Q:

Product and price descriptions for three products from three different categories are given below. You can choose one Product (Product 1, 2, OR 3) and create at least TWO segmentation profiles for...

Q:

5. Indifference curves. Assume that the consumer purchases only two goods, x and y. Based on the information in each of the following parts, sketch a plausible set of indifference curves (that is,...

Q:

f(x;0,B) = {{z+B)Q+T Question 9. Let X be a random variable having density given by if r > 0 elsewhere where a > 0 and 8 >0 are parameters. (a) (5 pts) If a > 0, show that B E[X] = Q- -1 (b) (5 pts)...

Q:

Problem 14-12 Marking-to-Market (LO2, CFA2) You are long 11 gold futures contracts, established at an initial settle price of $1,485 per Ounce, where each contract represents 100 troy ounces. Your...

Q:

Review the t test scenarios the three different approaches of t tests: Independent sample t test Paired sample t test One sample t test Analysis of your t test results for each research scenario and...

Q:

Question 3 Battery manufacturers compete on the basis of the amount of time their products last in scientific calculators. A manufacturer of such batteries has observed that the lifespan for their...

Q:

A steel beam having a span of 6.4m is simply supported at its ends and is laterally unrestrained over its whole length. It supports a uniformly distributed permanent action (dead load) (G) of 13 kN/m...

Q:

You can use the sinking fund factor Group of answer choices to show the amount accumulated at the end of a specific period that will result from level periodic deposits. to show the deposit required...

Q:

Discuss the role of investment bankers in mortgage-backed securities and the secondary market.

Q:

Derive the expressions for the mean and variance of a geometric random variable with parameter p. (Formulas for infinite series are required.)

Q:

Suppose X has a hypergeometric distribution with N = 100, n = 4, and K = 20. Determine the following: (a) P(X = 1) (b) P(X =6) (c) P(X =4) (d) Determine the mean and variance of X.

Q:

Suppose X has a hypergeometric distribution with N = 20, n = 4, and K = 4. Determine the following: (a) P(X = 1) (b) P(X =4) (c) P(X =2 (d) Determine the mean and variance of X.

Q:

Luther Industries has a dividond yield of 5% and a cost of equity capital of 10%. Luther Industries dividends are expected to grow at a constant rate indefinitely. The growth rate of Luther's...

Q:

a) why is the sampling distribution approximately normal? b) what is the mean of the sampling diatribution? c) what is the standard deviation of the sampling distribution? d) Assuming that the...

Q:

Free Cash Inc.'s cost of capital is estimated to be 9 percent. The free cash flows to the firm (FCFF) is estimated to be S4:750r S7:000: and S9:750 in each of the next three years. Free cash flows...