The random variable X can take on the values -5, 0, and 5, and the random...

The random variable X can take on the values -5, 0, and 5, and the random variable Y can take on the values 20, 25, and 30. The joint probability distribution of X and Y is given in the following table: Y 20 25 30 X -5 0.15 0.02 0.06 0 0.08 0.05 0.05 5 0.32 0.10 0.17 a. Describe in words and notation the event that has probability 0.17 in the table. . b. Calculate the marginal distribution of X and the marginal distribution of Y. c. Calculate the population mean μ for X

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orchestra answered 2 years ago

The random variable X can take on the values 1, 2 and 3 and the random...

The random variable X can take on the values 1, 2 and 3 and the random variable Y can take on the values 1, 3, and 4. The joint probability distribution of X and Y is given in the following table: Y 1 3 4 X 1 0.1 0.15 0.1 2 0.1 0.1 0.1 3 0.1 0.2 a. What value should go in the blank cell? b. Describe in words and notation the event that has probability 0.2 in the...

Suppose that random variable X 0 = (X1, X2) is such that E[X 0 ] =...

Suppose that random variable X 0 = (X1, X2) is such that E[X 0 ] = (µ1, µ2) and var[X] = σ11 σ12 σ12 σ22 . (a matrix) (i) Let Y = a + bX1 + cX2. Obtain an expression for the mean and variance of Y . (ii) Let Y = a + BX where a' = (a1, a2) B = b11 b12 0 b22 (a matrix). Obtain an expression for the mean and variance of Y . (ii)...

A continuous random variable X, has the density function f(x) =((6/5)(x^2)) , 0 ≤ x ≤...

A continuous random variable X, has the density function f(x) =((6/5)(x^2)) , 0 ≤ x ≤ 1; (6/5) (2 − x), 1 ≤ x ≤ 2; 0, elsewhere. (a) Verify f(x) is a valid density function. (b) Find P(X > 3 2 ), P(−1 ≤ X ≤ 1). (c) Compute the cumulative distribution function F(x) of X. (d) Compute E(3X − 1), E(X2 + 1) and σX.

5. Consider a random variable with a piecewise-constant PDF f(x) = 1/2, 0 < x ?...

5. Consider a random variable with a piecewise-constant PDF f(x) = 1/2, 0 < x ? 1, 1/8, 1 < x ? 3, 1/12 , 3 < x < 6. Design the simulation algorithm using the inverse-transform method.

write a for loop that uses the loop control variable to take on the values 0...

write a for loop that uses the loop control variable to take on the values 0 through 10. In the body of the loop, multiply the value of the loop control variable by 2 and by 10. Execute the program by clicking the Run button at the bottom of the screen. Is the output the same?

For a random variable X with a Cauchy distribution with θ = 0 , so that...

For a random variable X with a Cauchy distribution with θ = 0 , so that f(x) =(1/ π)/( 1 + x^2) for -∞ < x < ∞ (a) Show that the expected value of the random variable X does not exist. (b) Show that the variance of the random variable X does not exist. (c) Show that a Cauchy random variable does not have ﬁnite moments of order greater than or equal to one.

The probability distribution of a discrete random variable x is shown below. X 0 &

The probability distribution of a discrete random variable x is shown below. X 0 1 2 3 P(X) 0.25 0.40 0.20 0.15 What is the standard deviation of x? a. 0.9875 b. 3.0000 c. 0.5623 d. 0.9937 e. 0.6000 Each of the following are characteristics of the sampling distribution of the mean except: a. The standard deviation of the sampling distribution of the mean is referred to as the standard error. b. If the original population is not normally distributed, the sampling distribution of the mean will also...

Does a continuous random variable X exist with E(X − a) = 0, where a is...

Does a continuous random variable X exist with E(X − a) = 0, where a is the day of your birthdate? If yes, give an example for its probability density function. If no, give an explanation. (b) Does a continuous random variable Y exist with E (Y − b) 2 = 0, where b is the month of your birthdate? If yes, give an example for its probability density function. If no, give an explanation.

1. Let X be random variable with density p(x) = x/2 for 0 < x<...

1. Let X be random variable with density p(x) = x/2 for 0 < x < 2 and 0 otherwise. Let Y = X^2−2. a) Compute the CDF and pdf of Y. b) Compute P(Y >0 | X ≤ 1.8).

5. For each random variable defined here, describe the set of possible values for the variable,...

5. For each random variable defined here, describe the set of possible values for the variable, and state whether the variable is discrete. ( a) X = number of unbroken eggs in a randomly chosen standard egg carton (b) Y = number of students on a class list for a particular course who are absent on the first day of classes (c) Z = number of times a golfer has to swing at a golf ball before hitting it (d)...

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