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MATH 240: STATISTICS FOR BUSSINESS

Tutorial 1: Random Variables and Probability Distributions

1. A box contains two \$1 bills, three \$5 bills, one \$10 bill and three \$20 bills. Construct a probability distribution for the data and draw a graph.

2. Compute mean and variance of the following discrete probability distribution.

|x |0 |1 |2 |3 |
|P(x) |0.2 |0.4 |0.3 |0.1 |

3. The random variable X has the following distribution:

|x |P(X=x) |
|3 | |
|5 |0.3 |
|6 |0.2 |
|7 |0.4 |

a. Find P(X=3)

b. Find μ

c. Find σ2

4. Three fair coins are tossed. Let X be the number of heads that occur. Find the E(X), σ2 and σ for the random variable X.

5. A bank vice president feels that each saving account customer has, on average, three credits cards. The following distribution represents the number of credit cards people own. Find the mean, variance and standard deviation. Is the vice president correct?

|Number of cards, x |0 |1 |2 |3 |4 |
|P(x) |0.18 |0.44 |0.27 |0.08 |0.03 |

6. A public speaker computes the probabilities for the number of speeches she gives each week. Compute the mean, variance and standard deviation of the distribution shown.

|Number of speeches, x |0 |1 |2 |3 |4 |5 |
|P(x) |0.06 |0.42 |0.22 |0.12 |0.15 |0.03 |