Let discrete random variable X be the number of flips of a biased coin required to...

Let discrete random variable X be the number of flips of a biased coin required to get tails, where P(tails) = 1/3 .

a) Calculate the probability for every value of X from 1 to 10.

b) Sketch a plot of the p.m.f. of X for the first 10 flips.

c) Sketch a plot the c.d.f. of X for the first 10 flips.

Solutions

Expert Solution

#Code#Output

b) #c)

orchestra answered 1 year ago

Next > < Previous

Related Solutions

1. A coin is tossed 3 times. Let x be the random discrete variable representing the...

1. A coin is tossed 3 times. Let x be the random discrete variable representing the number of times tails comes up. a) Create a sample space for the event; b) Create a probability distribution table for the discrete variable x; c) Calculate the expected value for x. 2. For the data below, representing a sample of times (in minutes) students spend solving a certain Statistics problem, find P35, range, Q2 and IQR. 3.0, 3.2, 4.6, 5.2 3.2, 3.5...

A fair coin is flipped until a head appears. Let the number of flips required be...

A fair coin is flipped until a head appears. Let the number of flips required be denoted N (the head appears on the ,\1th flip). Assu1ne the flips are independent. Let the o utcon1es be denoted by k fork= 1,2,3, . ... The event {N = k} 1neans exactly k flips are required. The event {,v;;, k} n1eans at least k flips are required. a. How n1any o utcon1es are there? b. What is Pr[N = k] (i.e., the probability...

An unbiased coin is tossed four times. Let the random variable X denote the greatest number...

An unbiased coin is tossed four times. Let the random variable X denote the greatest number of successive heads occurring in the four tosses (e.g. if HTHH occurs, then X = 2, but if TTHT occurs, then X = 1). Derive E(X) and Var(X). (ii) The random variable Y is the number of heads occurring in the four tosses. Find Cov(X,Y).

In a sequence of independent flips of a fair coin, let N denote the number of...

In a sequence of independent flips of a fair coin, let N denote the number of flips until there is a run of three consecutive heads. Find P(N ≤ 8). (Should write out transition matrix.)

There is a fair coin and a biased coin that flips heads with probability 1/4.You randomly...

There is a fair coin and a biased coin that flips heads with probability 1/4.You randomly pick one of the coins and flip it until you get a heads. Let X be the number of flips you need. Compute E[X] and Var[X]

The discrete random variable X is the number of passengers waiting at a bus stop. The...

The discrete random variable X is the number of passengers waiting at a bus stop. The table below shows the probability distribution for X. What is the expected value E(X) for this distribution? X 0 1 2 3 Total P(X) .20 .40 .30 .10 1.00 Answer the following questions using the given probability distribution. Expected value E(X) of the number of passengers waiting at the bus stop. Probability that there is at least 1 passenger at the bus stop. Probability...

A coin is tossed three times. X is the random variable for the number of heads...

A coin is tossed three times. X is the random variable for the number of heads occurring. a) Construct the probability distribution for the random variable X, the number of head occurring. b) Find P(x2). c) Find P(x1). d) Find the mean and the standard deviation of the probability distribution for the random variable X, the number of heads occurring.

Bob flips a coin 3 times. Let A be the event that Bob flips Heads on...

Bob flips a coin 3 times. Let A be the event that Bob flips Heads on the first two flips. Let B be the event that Bob flips Tails on the third flip. Let C be the event that Bob flips Heads an odd number of times. Let D be the event that Bob flips Heads at least one time. Let E be the event that Bob flips Tails at least one time. (a) Determine whether A and B are...

Let X be a random variable that is equal to the number of times a 5...

Let X be a random variable that is equal to the number of times a 5 is rolled in three rolls of a fair 5-sided die with the integers 1 through 5 on the sides. What is E[X2 ]? What is E2 [X], that is, (E[X])2 ? Justify your answers briefly

2. Bob flips a coin 3 times. Let A be the event that Bob flips Heads...

2. Bob flips a coin 3 times. Let A be the event that Bob flips Heads on the first two flips. Let B be the event that Bob flips Tails on the third flip. Let C be the event that Bob flips Heads an odd number of times. Let D be the event that Bob flips Heads at least one time. Let E be the event that Bob flips Tails at least one time. (a) Determine whether A and B...

Subjects