Chapter 5, Problem 5.18LB

Assume x is exponentially distributed with a mean of 4. Find: a.P(X=2) b.P(X<2) c.P(X>=2) d.P(2 < X < 4)

Suppose the value of a stock varies each day from $12 to $27 with a uniform distribution.  Find σ

4d.) Draw the graphs. Round your final answers up to 6 decimal places, if applicable. Give the correct units.

9. Assume that X has an exponential distribution. If Var (4-4)=20. Then E(X) is a. 20 b.0 c. 5 d. 10 e. None 10. The variable X has a uniform distribution and

Suppose a sample Y1, ..., Yn is selected from an exponential distribution with E (Yi) = θ and V (Yi) = θ2. Let θˆ be an estimator of the mean, θ.1. Explain what a parameter is. What is the parameter of interest in this case?2. Name the properties of a good estimator and explain, shortly, what is meant by each. (a)(b) (c)3. Given the properties you discussed in (2) and the parameter of interest identified in (1), what estimator would you propose?4. What would the sampling distribution of this estimator be? Why?

*2. Let log Y the median of Y). ~ N (u, o2). Find the distribution of Y and show that P(Y < eH) = 0.5 (i.e., el is

Q60. Define gamma distribution with parameters 5 and 7 and obtain its moment generating function. Hence or otherwise find its mean and variance.

Please answer letters d. and e.

H[8/15, 2:46 PM] Destiny: 6. The following table shows scores obtained in an examination by B.EdJHS Specialism students. Use the information to answer the questionsthat follow:Score 20-24 25-29 30-34 35-39 40-44 45-49 50-54 55-59 60-64 65-69Frequency 10 4 10 20 30 15 3 2 1 5 a. Construct a cumulative frequency curve for the data.b. Find the;i. inter-quartile range.ii. 70th percentile class scores.iii. probability that a student scored at most 50 on the examination