Find the value of c, the expectation of X, and the variance of X. Let X be a random variable with probability density function1. Find the value of c.2. Find the expectation E[X] of X.3. Find the variance Var(X) of X.(c, E[X], Var(X)) = (______________).fx(x) = cx if 0≤x≤ 3,0 Otherwise.

The provided information is as follows:The is a random variable with the probability density…

Answered: 1. Find the value of c. 2. Find the…

1. Find the value of c. 2. Find the expectation E[X] of X. 3. Find the variance Var(X) of X. (c, E[X], Var(X)) = (______________). 0 Otherwise. 5

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

See similar textbooks

Related questions

Q: 2. In the random effects model, the null hypothesis is about the variance of the effects of the…

Q: Let X and Y be independent random variables with means ux, μy and variances o, oy. Find an…

A: Given: Random variable x and y are independent with means ux, uy , varience σ2(x) and σ2(y) E(x)=…

Q: Company A claims that the variance of the life of its appliances is less than the variance of the…

A: Company A claims that the variance of the life of its appliances is less than the variance of the…

Q: Let X and Y be identically distributed with mean 3 and variance 25. (a) If X and Y are uncorrelated,…

A: Let X and Y be identically distributed with mean 3 and variance 25 . Therefore, EX=3, EY=3, VarX=25…

Q: You and a friend play a game where you each toss a balanced coin. If the upper faces on the coins…

A: Let be the winnings price on a single play of the game.If both coins show tails, he wins .If both…

Q: Suppose X takes the value 1 with probability P, and the value 0 with probability (1-P). The…

A: Variance formula is:

Q: Calculate L = E(Ä|X1) and find its variance. Is the variance of L smaller than the variance of Ä? Is…

Q: POPULATION MEAN POPULATION VARIANCE XX - a) POPULATION STANDARD DEVIATION E(x-)

Q: Suppose that the random variable X measures the number of hot dogs purchased in a food court in an…

A: CorX,Y=0.75VX=VY=36W=2X+3Y

Q: Problem 5: Suppose that 70% of men and 30% of women in a state support the incumbent candidate of…

A: Number of men workers = 70% Number of women workers = 30% 500 people are surveyed at random

Q: Let X have a mean of 132 and a variance of 32. Define Y=X² + 2X+1. Compute the (a) mean and (b)…

Q: a. Find the mean and variance of the probability distribution. b. Interpret the mean and the…

A: here given discrete probability distribution of X=number of android phones

Q: The random variable Y has the Poisson distribution with a mean of 50. (a) What is the variance of Y?…

A: Let Y have a Poisson distribution with a mean of 50.The PMF of Poisson distribution with a mean of…

Q: Jessica hypothesizes that giraffes will look longer at human infants than at adults. In her zoo, she…

A: It is given that Jessica hypothesizes that giraffes will look longer at human infants than at adults…

Q: Express the quartiles, Q1, Q2, and Q3, of a normally distributed variable in terms of its mean, µ,…

A: First Quartile (Q1)From the given information the first quartile is represented by 25th percentile…

Q: Suppose that the probability that a patient admitted in a hospital is diagnosed with a certain type…

Q: Let X and Y be independent random variables with means x,y and variances o, oy. Find an expression…

Q: Let X; be independent Uniform(-10,10) random variables, for i=1, 2, ..., 5. Let Y = X₁+X₂+...+X5.…

A: Let be independent random variable follows uniform(-10, 10) distribution for i=1, 2,....., 5the…

Q: e) Determine the mean and variance of W = 3X,-2X2+5

A: Given: Consider X1- Customer will spend more than RM50 at counter 1. It follows Binomial…

Q: Let X-G(6,0.3) Find the variance of the gamma distribution.

Q: A barber expects to get between zero and six customers per hour in his barber shop. The probability…

A: Solution-: We have following table: X P(X) 0 0.15 1 0.07 2 0.29 3 0.26 4 0.13 5 0.09…

Q: You know that Z = 5X + 17. The expected value of X is 4 and its variance is 3. What are the mean and…

A: Given that : Z = 5x + 17 E(x) = 4 and var ( x) = 3 By using expectations properties we get

Q: Suppose that for a particular computer salesperson, the probability distribution of x = the number…

A: a) The random variable x defines the number of systems sold in 1 month.

Q: If the variances for independent random variables X and Y is Var(X)=0.94 and Var(Y)=4.22 then Var…

A: The given variances for independent random variables X and Y are Var(X)= 0.94 Var(Y) = 4.22 We have…

Q: find the mean, variance and standard deviation.

Q: What is the Discrete Variable Variance for the following numbers:x = 0 and P(X = x) = 0.19x = 1 and…

A: The objective of this question is to calculate the variance of a discrete random variable. Variance…

Q: (a) Among the next 210 customers, what are the mean and variance of the number who pay with a debit…

A: Consider the events A, B and C that represents the customers who pay with a credit card, debit card,…

Q: Find the variance of X + 3Y + Z + 6 in terms of the variances and covariances of X, Y, and Z.

A: Given: X + 3Y + Z + 6

Q: 0.3 and 0.4 respectively. Le variance of T is? 05

A: Given that V(A)=0.3 V(B)=0.4 T=5A-2B

Q: Customers at a gas station pay with a credit card (A), debit card (B), or cash (C). Assume that…

A: We have given that Customers at a gas station pay with a creditcard (A), debit card (B), or cash…

Question

Find the value of c, the expectation of X, and the variance of X.

Let X be a random variable with probability density function
1. Find the value of c.
2. Find the expectation E[X] of X.
3. Find the variance Var(X) of X.
(c, E[X], Var(X)) = (______________).
fx(x) = cx if 0≤x≤ 3,
0 Otherwise.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1: Given information

VIEW

Step 2: Calculate value of c

VIEW

Step 3: Calculate mean

VIEW

Step 4: Calculate variance

VIEW

Solution

VIEW

Step by step

Solved in 5 steps with 16 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

Give an explanation why this statement is either true or false: Portfolio contains n assets. Therefore, portfolio variance for this portfolio is the function of 2n covariances and n variances.
Assume that you have a random variable X which is binomially distributed, and someone told you that the mean of this variable is (6) and variance is (4.2). Find P(X=5).
Consider the following probability distribution function of X and Y: 1 2 0.35 0.05 Y 1 0.15 0.45 Find the variance of X and the variance of Y.
it is multichoice, thank you!
The mean of X is 5 and its SD is 3. The Mean of Y is -2 and its SD is 6. You are now being told they are independent. Find the value of each requested parameter A. The mean of T= -3x +20 is ___ B. The mean of W= Y - X is ___ C. The variance of D = X - 2Y is ___
Let G and H be two independent unbiased estimators of 0. Assume that the variance of G is two times the variance of H. Find the constants a andb so that aG + bH is an unbiased estimator with the smallest possible variance for such a linear combination.
Consider the bivariate distribution for the random variables x and y. The correlation coefficient of x and y is the covariance a. Consider the bivariate distribution for the random variables x and y. The correlation coefficient of x and y is the covariance b. multiplied by the product of the standard deviations for x and y. c. multiplied by the standard deviation of y and divided by the standard deviation of x. d. multiplied by the standard deviation of x and divided by the standard deviation of y.
The random variables A and B have variances 0.2 and 0.5 respectively. Let T= 5A+2B. The variance of T is 6 a. True b. False <
- The mean and variance of a binomial distribution are 4 and 4 respectively. Find P(X 21).