**1. ** Compute the sampling distribution for two tosses of a fair coin; $X = 1$ for heads, and $X = 0$ for tails.

Answer
**2. ** Compute the sampling distribution for two tosses of a fair die; $X = 1$ for an even number, and $X = 0$ for an odd number.
**3. ** Compute the sampling distribution for two tosses of an unfair coin, where $P(H) = 0.25$ and $P(T) = 0.75;$ $X = 1$ for heads, and $X = 0$ for tails.

Answer
**4. ** Compute the sampling distribution for two tosses of a fair die, $X = 1$ for a $1$ or $2$ facing up, and $X = 0$ for any other number.
**5. **
Consider the following probability ditribution.

**$X$** | $0$ | $1$ | $5$ |

**$P(X=x)$** | $1/3$ | $1/3$ | $1/3$ |

**(a) **Find $μ.$
Answer

**(b) **Find the sampling distribution of the sample mean $\bar{x}$ for samples of size $n = 2.$
Answer

**(c) ** Show that $X-$is an unbiased estimator for $μ.$
Answer

**6. **
Consider the following probability ditribution.

**$X$** | $-1$ | $0$ | $3$ |

**$P(X=x)$** | $1/4$ | $1/4$ | $1/2$ |

**(a) **Find $μ.$

**(b) **Find the sampling distribution of the sample mean $\bar{x}$ for samples of size $n = 2.$

**(c) ** Show that $X-$is an unbiased estimator for $μ.$

**7. **Select the correct options to make the following sentence correct.

**8. **Select the correct options to make the following sentence correct.

**9. ** According to a 1995 study, the mean family income in the US was $\$38,000$ with a standard deviation of $21,000.$ If a consulting agency surveys 49 families at random, what is the probability that it finds a mean family income of more than $\$41,500$?
Answer
**10. ** According to coach Simon, the average height of male soccer players in the US is normally distributed with mean $1.79m$ with a standard devation of $0.04m.$

**(a) ** In a randomly selected soccer team of 11 players, what is the probability that the averge height of the players is less than $1.77m$?

**(b) **In view of the small sample size, must you make any additional assumptions to justify the answer? Explain

Answer

Last Updated:*March, 1998*
Copyright © 1998 StefanWaner and Steven R. Costenoble