Question

Continuous distributions: Generate and store in column c1 10,000 values from the uniform distribution on the interval [4,8] as follows: random 10000 c1; uniform 4 8. (Do not forget the ”dot”) [3] a. Use mean command to find the sample mean ¯x of these data, ¯x=————- Note: The mean µ of a uniform distribution over an interval [a, b] is simply the middle of this interval, i.e. µ = (a + b)/2. [3] b. What is the mean µ of the uniform distribution on the interval [4,8]? µ=———- Compare µ to the value ¯x you found in part a). ———————– Generate and store in column c2 1,000 values from exponential distribution with mean 7 as follows: random 1000 c2; exponential 7. Note: The mean µ and the standard deviation σ of such distribution are both equal to the mean above. [3] c. Use desc command to find the sample mean ¯x and sample standard deviation s for these 1,000 data ¯x=———- and s =————– Are ¯x and s close to the value 7?———————– [3] d. Use Minitab to draw a histogram of the 1,000 values you generated from this exponential distribution. What is the shape of this distribution?———————–

Answer 1

a. Use mean command to find the sample mean ¯x of these data

Ans: ¯x=  5.9986

The mean µ of a uniform distribution over an interval [4, 8] is simply the middle of this interval, i.e.

µ =(4+8)/2=6

From the sample mean and actual mean of the uniform distribution, the two values are similar. Hence, we can conclude that the sample mean of the data is the estimator of the population mean.

The sample mean ¯x and sample standard deviation s for these 1,000 data are ¯x=6.767 and s =6.559. Yes, both ¯x and s are close to the value 7.

The histogram of the n=1,000 values generated from this exponential distribution with mean 7 is

The shape of this distribution is positive skewness.