A health-food store stocks two different brands of a certain type of grain. Let X = theamount (lb) of brand A on hand and Y = the amount of brand B on hand. Suppose thejoint pdf of X and Y isf(x, y) =kxy x ≥ 0, y ≥ 0, 20 ≤ x + y ≤ 300 otherwisea. Draw the region of positive density and determine the value of k.b. Are X and Y independent? Answer by first deriving the marginal pdf of eachvariable.c. Compute P(X + Y ≤ 25).d. What is the expected total amount of this grain on hand?e. Compute Cov(X, Y) and Corr(X, Y).f. What is the variance of the total amount of grain on hand?
A health-food store stocks two different brands of a certain type of grain. Let X = theamount (lb) of brand A on hand and Y = the amount of brand B on hand. Suppose thejoint pdf of X and Y isf(x, y) =kxy x ≥ 0, y ≥ 0, 20 ≤ x + y ≤ 300 otherwisea. Draw the region of positive density and determine the value of k.b. Are X and Y independent? Answer by first deriving the marginal pdf of eachvariable.c. Compute P(X + Y ≤ 25).d. What is the expected total amount of this grain on hand?e. Compute Cov(X, Y) and Corr(X, Y).f. What is the variance of the total amount of grain on hand?
A health-food store stocks two different brands of a certain type of grain. Let X = theamount (lb) of brand A on hand and Y = the amount of brand B on hand. Suppose thejoint pdf of X and Y isf(x, y) =kxy x ≥ 0, y ≥ 0, 20 ≤ x + y ≤ 300 otherwisea. Draw the region of positive density and determine the value of k.b. Are X and Y independent? Answer by first deriving the marginal pdf of eachvariable.c. Compute P(X + Y ≤ 25).d. What is the expected total amount of this grain on hand?e. Compute Cov(X, Y) and Corr(X, Y).f. What is the variance of the total amount of grain on hand?
A health-food store stocks two different brands of a certain type of grain. Let X = the amount (lb) of brand A on hand and Y = the amount of brand B on hand. Suppose the joint pdf of X and Y is f(x, y) = kxy x ≥ 0, y ≥ 0, 20 ≤ x + y ≤ 30 0 otherwise a. Draw the region of positive density and determine the value of k. b. Are X and Y independent? Answer by first deriving the marginal pdf of each variable. c. Compute P(X + Y ≤ 25). d. What is the expected total amount of this grain on hand? e. Compute Cov(X, Y) and Corr(X, Y). f. What is the variance of the total amount of grain on hand?
Definition Definition Probability of occurrence of a continuous random variable within a specified range. When the value of a random variable, Y, is evaluated at a point Y=y, then the probability distribution function gives the probability that Y will take a value less than or equal to y. The probability distribution function formula for random Variable Y following the normal distribution is: F(y) = P (Y ≤ y) The value of probability distribution function for random variable lies between 0 and 1.
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