Question

R.1 A random variable X is defined to be the difference between the higher value and the lower value when two dice are thrown. If they have the same value, X is defined to be zero. Find the probability distribution for X. R.3 Find the expected value of X in Exercise R.1. R.6 Calculate E(X²) for X defined in Exercise R.1. R.9 Calculate the population variance and the standard deviation of X as defined in Exercise R.1., using the definition given by equation (R.8) in the textbook. R.11 Using equation (R.9) in the textbook, find the variance of the random variable X defined in Exercise R.1. and show that the answer is the same as that obtained in R.9. (Note: You have already calculated E(X) in R.3 and E(X²) in R.6.) R.13 Suppose a variable Y is an exact linear function of X: Y = ? + ?X where ? and ? are constants. Demonstrate that the correlation between X and Y is equal to 1 or –1, according to the sign of ?. (This question is different from R.13 in the third edition text) Note: (R.8): var(X)=E[(X – ?x)²] and when X is discrete, it is equal to ?????(x? – ?x)²p? (R.9): var(X)=E(X²)– ?²x

          R.1 A random variable X is defined to be the difference between the higher value and the lower
value when two dice are thrown. If they have the same value, X is defined to be zero. Find the
probability distribution for X.

R.3 Find the expected value of X in Exercise R.1.

R.6 Calculate E(X²) for X defined in Exercise R.1.

R.9 Calculate the population variance and the standard deviation of X as defined in Exercise
R.1., using the definition given by equation (R.8) in the textbook.

R.11 Using equation (R.9) in the textbook, find the variance of the random variable X defined
in Exercise R.1. and show that the answer is the same as that obtained in R.9. (Note: You have
already calculated E(X) in R.3 and E(X²) in R.6.)

R.13 Suppose a variable Y is an exact linear function of X: Y = ? + ?X where ? and ? are
constants. Demonstrate that the correlation between X and Y is equal to 1 or –1, according to
the sign of ?. (This question is different from R.13 in the third edition text)

Note: (R.8): var(X)=E[(X – ?x)²] and when X is discrete, it is equal to ?????(x? – ?x)²p?
(R.9): var(X)=E(X²)– ?²x

R.1 A random variable X is defined to be the difference between the higher value and the lower
value when two dice are thrown. If they have the same value, X is defined to be zero. Find the
probability distribution for X.

R.3 Find the expected value of X in Exercise R.1.

R.6 Calculate E(X²) for X defined in Exercise R.1.

R.9 Calculate the population variance and the standard deviation of X as defined in Exercise
R.1., using the definition given by equation (R.8) in the textbook.

R.11 Using equation (R.9) in the textbook, find the variance of the random variable X defined
in Exercise R.1. and show that the answer is the same as that obtained in R.9. (Note: You have
already calculated E(X) in R.3 and E(X²) in R.6.)

R.13 Suppose a variable Y is an exact linear function of X: Y = ? + ?X where ? and ? are
constants. Demonstrate that the correlation between X and Y is equal to 1 or –1, according to
the sign of ?. (This question is different from R.13 in the third edition text)

Note: (R.8): var(X)=E[(X – ?x)²] and when X is discrete, it is equal to ?????(x? – ?x)²p?
(R.9): var(X)=E(X²)– ?²x

Added by Jonathon R.

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