2. Suppose that X has a (continuous) uniform distribution between 10 and 20. a. Compute the...

 

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2. Suppose that X has a (continuous) uniform distribution between 10 and 20. a. Compute the expected value E(X). b. Compute the variance Var(X). c. Compute P(X<12). d. Compute P(X> 12). e. Compute P(X< 8 or X> 22). 3. Suppose that X is an exponential random variable with mean 5. (The cumulative distribution function is F(x) = 1-e-x/5 for x ≥ 0, and F(x) = 0 for x < 0). a. Compute P(X > 5). b. Compute P(1.4 ≤ x ≤ 4.2). c. Compute P(1.4 < X < 4.2). 4. Suppose that 7.3, 6.1, 3.8, 8.4, 6.9, 7.1, 5.3, 8.2, 4.9, and 5.8 are ten observations from a normal distribution with unknown mean and unknown variance. Compute the sample mean, sample variance, and a 95 percent confidence interval for the population mean. Note: use the provided t table as needed. 2. Suppose that X has a (continuous) uniform distribution between 10 and 20. a. Compute the expected value E(X). b. Compute the variance Var(X). c. Compute P(X<12). d. Compute P(X> 12). e. Compute P(X< 8 or X> 22). 3. Suppose that X is an exponential random variable with mean 5. (The cumulative distribution function is F(x) = 1-e-x/5 for x ≥ 0, and F(x) = 0 for x < 0). a. Compute P(X > 5). b. Compute P(1.4 ≤ x ≤ 4.2). c. Compute P(1.4 < X < 4.2). 4. Suppose that 7.3, 6.1, 3.8, 8.4, 6.9, 7.1, 5.3, 8.2, 4.9, and 5.8 are ten observations from a normal distribution with unknown mean and unknown variance. Compute the sample mean, sample variance, and a 95 percent confidence interval for the population mean. Note: use the provided t table as needed.

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