Branching Processes: Show that if μ=1 then probability of extinction is 1.

It has been claimed that, for a penny minted in 1999 or earlier, the probability of observing heads upon spin- ning the penny is p = 0.30. Three students got together, and they would each spin a penny and record the num- ber X of heads out of the three spins. They repeated this experiment n = 200 times, observing 0, 1, 2, and 3 heads 57, 95, 38, and 10 times, respectively.

You have n = 200 data points: 0 appears 57 times, 1 appears 95 tmes, 2 appears 38 times and 3 appears 10 times. Test the hypothesis that this data came from binomial distribution. (Here you need to estimate the parameters of the binomial first.)

Find the probability that the sum is as stated when a pair of dice is rolled. (Enter your answers as fractions.) (a) odd and less than 5 (b) odd or less than 5

List the four laws of probability theory and express them mathematically.

how to do comparing empirical and theoretical probability on excel sheet

Suppose that the probability that a passenger will miss a flight is

0.0925

Airlines do not like flights with empty​ seats, but it is also not desirable to have overbooked flights because passengers must be​ "bumped" from the flight. Suppose that an airplane has a seating capacity of

59

passengers.

​(a) If

61

tickets are​ sold, what is the probability that

60

or

61

passengers show up for the flight resulting in an overbooked​ flight?

​(b) Suppose that

65

tickets are sold. What is the probability that a passenger will have to be​ "bumped"?

​(c) For a plane with seating capacity of

61

​passengers, how many tickets may be sold to keep the probability of a passenger being​ "bumped" below

55​%?

pointer 1 has 2 sections 50% red and 50% yellow.. pointer 2 has 3 sections 50% blue and 25% red and 25% yellow

A football player completes a pass 63.4 ​% of the time. Find the probability that​ (a) the first pass he completes is the second​ pass, (b) the first pass he completes is the first or second​ pass, and​ (c) he does not complete his first two passes.

In conducting a hypothesis test for a correlation, the correct probability distribution to use is the F distribution.

True

False

Utah State University recently randomly sampled ten students and analyzed grade point average (GPA) and number of hours worked off-campus per week. The following data were observed:

If the university wished to test the claim that the correlation between hours worked and GPA is negative, the following null and alternative hypotheses would be appropriate:

H_o: ρ < 0.0

H_a: ρ ≥ 0.0

T/F

When the correlation coefficient for the two variables was -0.23, it implies that the two variables are not correlated because the correlation coefficient cannot be negative.

True

False

A game designer claims that there is a 20% chance (or a probability value of 0.2) that an intermediate player will complete the fifth level of a game at the first trial. The game is tested by 8 players of intermediate skills. Assuming events are independent,answer the following questions:

a)What is the probability that only two out of 8 players will pass the game fifth level at the first trial? (NOTE: there are 28 different ways to select 2 players out of 8 players)

b)What is the probability that at least one player out of the 8 players will pass the game fifth level at the first trial?

c)What’s the probability that none of the 8 players will pass the fifth level at the first trial?