Question

Suppose that seven balls are selected at random without replacement from a box containing five red balls and ten blue balls. Let X denote the number of red balls drawn. (a) Give the distribution for X, stating all parameters clearly. (b) Give the closed form pmf for X. (c) Create a table describing the probability distribution for all possible outcomes of X. You may use R to calculate these probabilities, or do them by hand. (d) What number x of red balls has the highest probability of being drawn? (e) What is the probability that the number of red balls drawn will be more than 1 and less than four? (f) What are the mean and the variance of the number of red balls drawn? (g) Let X? denote the proportion of red balls in the sample, what are the mean and the variance of X?? Hint: X? = X/n.

          Suppose that seven balls are selected at random without replacement from a box containing five red balls and ten blue balls. Let X denote the number of red balls drawn.

(a) Give the distribution for X, stating all parameters clearly.

(b) Give the closed form pmf for X.

(c) Create a table describing the probability distribution for all possible outcomes of X. You may use R to calculate these probabilities, or do them by hand.

(d) What number x of red balls has the highest probability of being drawn?

(e) What is the probability that the number of red balls drawn will be more than 1 and less than four?

(f) What are the mean and the variance of the number of red balls drawn?

(g) Let X? denote the proportion of red balls in the sample, what are the mean and the variance of X??
Hint: X? = X/n.

Suppose that seven balls are selected at random without replacement from a box containing five red balls and ten blue balls. Let X denote the number of red balls drawn.

(a) Give the distribution for X, stating all parameters clearly.

(b) Give the closed form pmf for X.

(c) Create a table describing the probability distribution for all possible outcomes of X. You may use R to calculate these probabilities, or do them by hand.

(d) What number x of red balls has the highest probability of being drawn?

(e) What is the probability that the number of red balls drawn will be more than 1 and less than four?

(f) What are the mean and the variance of the number of red balls drawn?

(g) Let X? denote the proportion of red balls in the sample, what are the mean and the variance of X??
Hint: X? = X/n.

Added by Rosario T.

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