Random variables and probability distributions worksheet answer key

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Worksheet 2 - Random Variables

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Answer: No, the total of P(X) is less than 1.

Answer: Yes, the total of P(X) is equal to 1.

Answer: No, the total of P(X) is over 1.

AP Stats

Ch. 7

Discrete Probability Distributions Worksheet

1. You flip four coins. Let X, the random variable, be the number of heads on all four

coins.

a. List the sample space for the experiment.

Answer: S= {HHHH, HHHT, HHTH, HHTT, HTHH, HTHT, HTTH, HTTT, THHH,

THHT, THTH, THTT, TTHH, TTHT, TTTH, TTTT}

b. What are the possible values for x?

Answer: Possible values of X= {0, 1, 2, 3, 4}

c. Is the random variable, x, continuous or discrete?

Answer: Discrete

d. Construct a probability distribution for this experiment.

Answer:

2. Determine if the following are probability distributions (if no, state why).

a. X 3 6 9 12 15

P(X) 4/10 2/10 1/10 1/10 1/10

b. X 1 2 3 4 5

P(X) 3/15 1/15 1/15 4/15 6/15

c. X 20 30 40 50

P(X) 1.1 0.2 0.9 0.3

Discrete Probability Distributions Worksheet

1. You flip four coins. Let X, the random variable, be the number of heads on all four

coins.

a. List the sample space for the experiment.

Ans: S= {HHHH, HHHT, HHTH, HHTT, HTHH, HTHT, HTTH, HTTT, THHH, THHT,

THTH, THTT, TTHH, TTHT, TTTH, TTTT }

b. What are the possible values for x?

Ans: Possible values of X = { 0, 1, 2, 3, 4 }

c. Is the random variable, x, continuous or discrete?

Ans: Discrete

d. Construct a probability distribution for this experiment.

X012 34

P(X)1/164/166/164/161/16

2. Determine if the following are probability distributions (if no, state why).

a. X3691215

P(X)4/102/101/101/101/10

b. X12345

P(X)3/151/151/154/156/15

c. X20304050

P(X)1.10.20.90.3

No. The total of the p(x) is less than 1

Yes, The total of p(x) is equals to 1

No. The total of p(x) is over 1