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. l. https://docs.google.com/fo YO 4.4 O 3.96 O 1.8 نقطة واحدة Let X denote the number of colleges where you will apply after your results and P(X =x) denotes your probability of getting admission in x number of colleges. It is given that if x = 0 or 1 if x = 2 if x 3 or 4 otherwise kx, 2kx, P(X = x) 3= %3D k(5 - x), 0, Where k is a positive constant. Then the probability that you will get admission in at most 2 colleges is 0.625

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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.

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TABLE 3: Number of packs with X number of RED candy x (Red Candy) 7 8 9 10 11 Total f (Pack) 3 5 3 3 1 15 Based on Table 3, find the probability that the number of red candy is: Less than the mean of X More than or equal to the mean of X Between and (E (X) - 1) and (E (X) + 1)

A risk averse individual faces uncertainty with two outcomes: good, bad. Theindividual has income $1260 at good and $840 at bad outcome. The probability of good outcome is 5/7 (so the probability of bad outcome is 1 – 5/7 = 2/7). The individual can buy any nonnegative x units of insurance. Every unit of insurance has price $p and it pays $1 in the event of bad outcome. In this insurance market, the unit price of insurance is known to be p = 2/3. (a)Suppose the individual buys x units of insurance. Determine the individual's net income under good income, net income under bad income and the average net income. Draw these three in a diagram as functions of x.    (b) For the individual: (i) compare full insurance with over insurance and (ii) compare full insurance with partial insurance. Then determine best choice of insurance for the individual.

A class contains 40 students. The probability of failing in one of the courses for each student is 0.03, but there is no chance to fail in more than one course. You know that a student failed in a course, the probability that the fail reason in non-attendance is 0.04. All other fail reasons are low average. The examinations are private, so the results are mutually independent. Let X and Y be the numbers of failed students due to non-attendance and due to low average, respectively, in that class this semester. Find the joint MGF

Answers must be in 4 decimals |1. Ben plans to enforce speed limits using radar traps at 4 different locations within the campus. The radar traps at each of the locations L1, L2, L3, and L4 are operated 40%, 30%, 30%, and 20% of the time, and if a person who is speeding on his way to work has probabilities of 0.2, 0.1, 0.5, and 0.2, respectively, of passing through these locations, what is the probability that he will not receive a speeding ticket? 2. Barangay Scout Fernandez has one fire truck and one ambulance available for emergencies. The probability that the fire truck is available when needed is 0.95, and the probability that the ambulance is available when called is 0.90. in the event that there is a fire in the barangay, find the probability that both the ambulance and the fire truck will be available.