A continuous random variable X has probability density function fx (x) given by fx(x) = k (2 – x)(x – 5), 25x55, = 0, elsewhere. %3! Find the value of k, and hence deduce the mean and variance of X. What are the valt mode and median of the distribution of X?

Q: Sam is practising free-throws in basketball. She has a 4/5 chance of scoring each time she shoots…

A:

Q: Let X be a random variable with E[X]=2, Var(X)= 4. Compute the expectation and variance of 3– 2X .

A: Solution-: Given: E(X)=2, Var(X)=4 Our aim to find, (a) E(3-2X)=? and  (b) Var(3-2X)=?

Q: 4. Suppose A and B are events in a sample space S with probabilities 0.8 and 0.7, respectively.…

A: Given that  P(A)=0.8   , P(B)=0.7  and  P(A ∩ B)=0.6

Q: In statistics test, students finish the test in between 80 minutes, at earliest, and 120 minutes, at…

A: What is the probability that the next student will finish the test between 85 and 95 minutes.

Q: a. What is the probability that a bulb is defective? b. Hence, what is the probability that two or…

A: here given , 1. Twelve electric bulbs are drawn independently every hour from a production line at a…

Q: Please find the numerical value of the area under the normal curve given the following information:…

A: Solution-: Let, X- be the standard normal random variable We want to find the numerical value of the…

Q: Two six-sided dice are rolled. What is the probability that the two dice land on even numbers or the…

A:

Q: Q. 8. What is the chance that a. leap year selected at random il contain 53 Sundays? [Hint : A leap…

A: The answer is attached below,

Q: from a deck of 52. A number card is one with value 2, 3, 4, 5, 6,7,8,9 or 10 so there are 36 number…

A:

Q: What is the appropriate t critical value for each of the fol- lowing confidence levels and sample…

A: We have given that the confidence interval and sample sizes for different parts. Here, need to find…

Q: Q 5. If U = {1, 2, 3, 4, 5, 6, 7, 8}, A = {1, 3, 5, 7}, B ={1, 2, 3, 5, 6, 7, 8}; werify that (AU BY…

A:

Q: is 6/9 and 12/18 equivalent

A: We have given that,  Is 6/9 and 12/18 equivalent?

Q: How many ways are there to assign 100 different diplomats to five different conti- nents if 10…

A:

Q: A deck consist of 3 Jacks, 3 Queens and 3 Kings of different suit. What is the probability of…

A: No: of  possible outcomes=taking 3 cards from 9 cards…

Q: The probability that a physician correctly diagnoses a particular illness is 0.7. Given that the…

A:

Q: Victoria encounters another challenge in the game. If she zaps a target in one try, Victoria gets a…

A: Given that, Victoria encounters challenge in the game. If she zaps a target in one try, Victoria…

Q: (b) Alice and Bob are playing a game of chance consisting of repeated rounds in which each has an…

A: After 16 rounds, Alica won 9 rounds Bob win 7 rounds We have to tell,  in next three round,…

Q: A test of 50 questions can be answered by letters A, B, C and D. Find the probability that exactly…

A: Solution-: A test of 50 questions can be solved by letters A, B, C and D.  Find P(exactly 30 of the…

Q: ion för drivers pulled-over by the g use before and after taking completing a tre blem-solving…

A: Cohen's effect is a popular metric used in psychological studies.  The Interpretation of the effect…

Q: Why is the answer for ii) not (3/9)*(4/9)?

A: We need to answer, why in part(ii) , P(BG) is not equal to (3/9)(4/9).

Q: The average number of acres burned by forest and range fires in a large New Mexico county is 4,300…

A:

Q: A deck consist of 3 Jacks, 3 Queens and 3 Kings of different suit. What is the probability of…

A: Given Information: No. of Jacks=03No. of Queens=03No. of Kings=03Total cards=09

Q: Which of the following is NOT an assumption of the Binomial distribution?

A: here use basic of binomial distribution

Q: Let X and Y have the joint probability distribution as following Y 0 1 3 a 0.2 0.1 0.3 0.2 0.1 (1)…

A: For the given data Find all the required

Q: D. Given o = 4.5 and u = 30, find the raw scores of the following. Show your complete and neat…

A:

Q: Use the binomial theorem to show that for all integers n 2 1, 3" = (6) + 2 (4) + 2° (") -

A:

Q: tics we deal with differ. own words, explain anc

A: What is variable : The variable is an algebraic terminology that indicate the undetermined value…

Q: Which of the following statements is NOT correct? Obtaining a SRS is generally more costly than…

A: Here we want to know incorrect statement

Q: 6. A class for engineers consists of 25 industrial, 10 mechanical, 10 electrical and 8 civil…

A: The answer is attached below,

Q: Q2/ Clothes manufacturing machine, the probability of appearing damaged products is C At the…

A:

Q: The table shows the estimated distribution of injury severity by child passenger. What is the…

A: Given data: Injury severity <1 Year 1 to 3 Years 4 to 7 Years Row total No injury 545786…

Q: (Note: Choices given in the dropdown list are rounded.) SciTool is now bidding for another contract.…

A:

Q: by fa (b - x), 0sxsb, 10, fx(x) = otherwise. Find the values of a and b.

A: Solution

Q: Medical researchers are interested in determining the relative effectiveness of two drug treatments…

A: a) Denote μ1, μ2 as the means number of days until remission after treatment 1 (1st population) and…

Q: 1. Determine the value of C that makes the function f(x,y) = c(x +y) a joint probability density…

A:

Q: (a) Find a sufficient statistic for 0. (b) Show that the sufficient statistic (found in part (a)) is…

A:

Q: Let X denotes the reaction time, in seconds; to a certain stimulants and Y denote the temperature at…

A:

Q: Trends in fashion have signaled the emergence of green as the color of the century. It ranked third…

A:

Q: Could you please explain the integration part? It's not clear to me how reached to the answer

A:

Q: Several months ago while shopping, I was interviewed to see whether or not I'd be interested in…

A: a)   Consider that p1, p2 is the true proportions of mall shoppers in author’s market category and…

Q: 1. Express E-1 k |3* in closed form (without using a summation sign or ellipsis).

A:

Q: Avery sets up a passcode on her tablet, which allows only seven-digit codes. She has heard that It's…

A: Given Number of ways to have seven digit code from these 6 digits

Q: 3. Suppose Chelsea has the following utility function over sure wealth: v (y) = In y (a) Consider…

A: the expected amount won from the lottery is calculated as E(Win amount) = (1/3) x 2 + (2/3) x 8…

Q: À survey of 1000 people asked whether they wear eyeglasses while driving. These people were also…

A:

Q: For a certain random variable X it is known that E[X]=2, Var(X)=3. What E[x']?

A:

Q: 4. Upper confidence limit 0.820 Lower confidence limit 0.490 5. Upper confidence limit 0.715 Lower…

A:

Q: (a) Var(X + Y ) = Var(X)+ Var(Y) (b) Ε(XY) - (EX) (EYΥ) (c) E(X + Y ) = EX+ EY

A: Since we answer up to three subparts of a problem, we'll be answering the first three sub parts…

Q: The following observations are on stopping distance (ft) of a particular truck at 20 mph under…

A:

Q: The data that follow represent the yield on 90 consecutive batches of ceramic substrate to which a…

A: