Consider the following CDF: a) Sketch the graph of F(x) x<0 F(x)=(x+1) 0≤x≤1 x ≥ 1 b) Find the following probabilities: i. P(X = 0) ii. P(X = 1) iii. P(0X≤0.5) iv. P(0 ≤ X ≤0.5] v. P(0.5 < X < 1)

A branch of a certain bank has six ATMs. Let X represent the number of machines in use at a particular time of day. The cdf of X is as follows: F(X) = (b) Calculate the following probabilities directly from the cdf: (a) p(2), that is, P(X = 2) (c) 0 x 3) P(2 ≤x≤5) P(2 < X <5)

The value of Fcalc increases as A. variability due to chance decreases B. variability due to chance increases C. as the number of observations in each group decreases D. cannot be determined since F is fixed

Exercise 4.1.4 in Applied Statistics & Probability for Engineers, 7th Ed.Suppose that f (x) = x / 8 for 3 < x < 5. Determine the following probabilities:a. P(X < 4) b. P(X > 3.5) c. P(4 < X < 5) d. P(X < 4.5) e. P(X < 3.5 or X > 4.5).

A contractor is interested in the total cost of a project on which he intends to bid. He estimates that materials will cost Kshs. 250,000/= and that his labor will be Kshs. 9,000/= per day. If the project takes X days to complete, the total labor cost will be 9,000X shillings and the total cost of the project in shillings will be: C = 250,000 + 9000X. The contractor forms subjective probabilities of likely completion times for the project as shown below.   Completion Time (X) days 10 11 12 13 14 Probability 0.1 0.3 0.3 0.2 0.1   Required Find the mean and variance for the completion time X.  Find the mean, variance and standard deviation for total cost.

Suppose that a decision maker's risk atitude toward monetary gains or losses x given by the utility function(x) = (50,000+x) 34/2. Suppose that a decision maker has the choice of buying a lottery ticket for $5, or not. Suppose that the lottery winning is $1,000,000, and the chance of winning is one in a thousand. Then..... O The decision maker should not buy the ticket, as the utility from not buying is 223.6, and the expected utility from buying is 223.59. The decision maker should not buy the ticket, as the utility from not buying is 223.6067, and the expected utility from buyingis 223.6065. O The decision maker should buy the ticket, as the utility from not buying 223.60, and the utility from buying is 224.4. The decision maker should buy the ticket, as the utility from not buying 223.6065, and the utility from buying is 223.6067.

Ezio just conducted a Chi-Square Goodness of Fit Test to determine if a sample of automobile manufacturers produce the expected distribution of 2-door sedans, 4-door sedans, SUVs, and trucks. The results of his test are: [X2(4) = 8.35, p = 0.36]. Identify the correct interpretation below.   A. Only some of the manufacturers in the sample produce a distribution of automobiles that is equal to what was expected B. The sample of manufacturers produce a distribution of automobiles that is significantly different from what was expected C. Only some of the manufacturers in the sample produce a distribution of automobiles that is different from what was expected D. The sample of manufacturers produce a distribution of automobiles that is equal to what was expected

Chapter 5: Uniform Distribution Question 2 Births are approximately Uniformly distributed between the 52 weeks of the year. They can be said to follow a Uniform distribution from 1 to 53 (a spread of 52 weeks). Round answers to 4 decimal places when possible.

How were the correct answers of 0.1251 and 0.0313 attained?

Use the tables provided to give your best estimate to the 6. probabilities: а. Р(Z> 1.9) b. P(ti, >1.9) c. P(Xs > 42.1) d. P(F,14 >1.8)