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 nature reserve has one bird of an uncommon species which frequents the large expanse of reed beds there. It is found that if a birdwatcher arrives at the path adjoining the reed beds, the probability that he or she is still waiting there to see the bird a time y later, where y is measured in minutes, is ·c ²²³ + 2 y c , y ≥0. 3 Find the probability that a birdwatcher spends between 2 and 4 minutes waiting to see the bird, and the mean and variance of the time that he or she waits there.

Determine the following probabilities: P(X > 0.25, Y 0.25, Y 0.25, Y 0.25, Y < 4.5) = 1/2 P(Y < 1.5) = 2/3

Need help with this Intro to probability and statistics homework problem. Below the homework problem is the answers from the textbook. Make sure your handwriting is neat and readable.

Suppose that the probabilities are 0.4, 0.3, 0.2, and 0.1, respectively, that 0,1,2 and 3 power failures will hit a certain subdivision in any given year. If X represents the no. of power failures hitting this subdivision given g(x) = 5x + 3, find E[g(x).

Consider the following function for a value of k.f(x) ={3kx/7,  0 ≤ x ≤ 1 3k(5 − x)/7 ,   1 ≤ x ≤ 30, otherwise.Comment on the output of these probabilities below, what will be theconclusion of your output.(i)Evaluate k.(ii)find (a) p(1 ≤ x ≤ 2) (b) p(x > 2). (u) p(x ≤ 8/3).

Suppose a professional basketball player historically makes 39% of his three-point field goals. After a rigorous off-season training, the .player makes 31 of his 75 three-point field goals Does this represent significant evidence that the player's three-point field goal shooting has ?improved The test statistic, is We cannot do the test statistic, because the .condition(s) is(are) not satisfied x-H O to (p-Po) Zo Po(1-po) V x-u to (d-po) Po(1-Po) 10 =

Please solve asap. Easy problem. 1st exercise.

Ana’s preferences are consistent with expected utility. Denote by u(x) her utility function for a monetary outcome £x, and suppose that she is strictly risk-averse. Ana currently faces the monetary lottery which pays: £A with probability pA; £B with probability pB; and £C with probability pC. Now suppose that Ana is made the following o§er. For each realization of the original lottery, another lottery will be executed according to which she wins an additional poundwith probability 1/2 and loses a pound with probability 1/2. Describe the lottery that Ana faces if she accepts the o§er by describing the new payo§s and probabilities over these payo§s. (b) Show that she rejects the o§er and explain why.

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.