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Consider an urn initially containing N є N balls. For n E Z+, let Xn be the number of balls in the urn after performing...
Consider an urn initially containing N є N balls. For n E Z+, let Xn be the number of balls in the urn after performing the following procedure n times. If the urn is non-empty, one of the balls is removed at random. A fair coin is flipped, and if the coin lands tails then the ball is returned to the urn. If the coin lands heads, the ball is not returned. If the urn is empty, then the coin...
2. SUPPLEMENTAL QUESTION 1 (a) Toss a fair coin so that with probability pheads occurs and...
2. SUPPLEMENTAL QUESTION 1 (a) Toss a fair coin so that with probability pheads occurs and with probability p tails occurs. Let X be the number of heads and Y be the number of tails. Prove X and Y are dependent (b) Now, toss the same coin n times, where n is a random integer with Poisson distribution: n~Poisson(A) Let X be the random variable counting the number of heads, Y the random variable counting the number of tails. Prove...
ASAP Exercise 6. This problem describes an experiment in which conditional probabilities are used to compute...
ASAP
Exercise 6. This problem describes an experiment in which conditional probabilities are used to compute "proper" probability. The experiment starts with two urns, Urn #1 contains 5 white marbles and 2 black marbles. Urn #2 contains 7 white marbles and 3 black marbles. One marble from each urn is drawn at random. (For each urn, the chance of each marble being drawn is the same.) Let T be the event that the two marbles are the same color. Let...
Answers for all questions please!! 8) A bag contains 10 red marbles and 8 green marbles....
Answers for all questions please!!
8) A bag contains 10 red marbles and 8 green marbles. Anne picks 3 replacement, and observes the color of each marble. The number of green binomial random variable. If we let success correspond to getting success probability, p?What is the number of trials? marbles at random, with 8) marbles, X, is a a green marble, what is the A) P- n3 Solve the problem. 9) One hundred people were asked, "Do you favor the...
28. In many problems about modeling count data, it is found that values of zero in the data are f...
28. In many problems about modeling count data, it is found that values of zero in the data are far more common than can be explained well using a Poisson model (we can make P(X 0) large for X ~ Pois(A) by making λ small, but that also constrains the mean and variance of X to be small since both are X). The Zero-Inflated Poisson distribution is a modification of the Poisson to address this issue, making it easier to...
1. (6 pts) Consider a non-negative, discrete random variable X with codomain {0, 1, 2, 3,...
1. (6 pts) Consider a non-negative, discrete random variable X with codomain {0, 1, 2, 3, 4, 5, 6} and the following incomplete cumulative distribution function (c.d.f.): 0 0.1 1 0.2 2 ? 3 0.2 4 0.5 5 0.7 6 ? F(x) (a) Find the two missing values in the above table. (b) Let Y = (X2 + X)/2 be a new random variable defined in terms of X. Is Y a discrete or continuous random variable? Provide the probability...
Suppose we toss a coin (with P(H) p and P(T) 1-p-q) infinitely many times. Let Yi be the waiting time for the first head so (i-n)- (the first head occurs on the n-th toss) and Xn be the number of hea...
Suppose we toss a coin (with P(H) p and P(T) 1-p-q) infinitely many times. Let Yi be the waiting time for the first head so (i-n)- (the first head occurs on the n-th toss) and Xn be the number of heads after n-tosses so (X·= k)-(there are k heads after n tosses of the coin). (a) Compute the P(Y> n) (b) Prove using the formula P(AnB) P(B) (c) What is the physical meaning of the formula you just proved?
Suppose...
Q1 ) A U Ac = Select one: a. S b. (A|B) c. P (A and...
Q1 ) A U Ac = Select one: a. S b. (A|B) c. P (A and B) = P (A∩B) d. A(OR)A e. P(A) ____________________________ Q2) wo dice are rolled, find the probability that the sum is less than 2 Select one: a. 1/36 b. 0/36 c. 2/36 d. 2/12 e. 4/12 ___________________________________ Q3) A die is rolled, find the probability that the number obtained is greater than 4 Select one: a. 0.167 b. 0% c. 50% d. 0.33 e....
3. An urn contains 2 black, 2 red, and 4 white marbles. You draw a marble...
3. An urn contains 2 black, 2 red, and 4 white marbles. You draw a marble at random. a) What is the sample space? b) What are all events (power Class)? c) What is the probability of each event? 4. A coin is tossed ten times and number of heads is noted. a) What is the probability that the number of heads is four? b) What is the probability of at least seven heads come? 6. X is a Binomial...
Exercise 8.26. Suppose I have an urn with 9 balls: 4 green, 3 yellow and 2...
Exercise 8.26. Suppose I have an urn with 9 balls: 4 green, 3 yellow and 2 white ones. I draw a ball from the urn repeatedly with replacement. (a) Suppose I draw n times. Let X., be the number of times I saw a green ball followed by a yellow ball. Calculate the expectation Ex, (b) Let y be the number of times I drew a green ball before the first white draw. Calculate E[Y]. Can you give an intuitive...
Consider an urn initially containing N є N balls. For n E Z+, let Xn be the number of balls in the urn after performing the following procedure n times. If the urn is non-empty, one of the balls is removed at random. A fair coin is flipped, and if the coin lands tails then the ball is returned to the urn. If the coin lands heads, the ball is not returned. If the urn is empty, then the coin...
2. SUPPLEMENTAL QUESTION 1 (a) Toss a fair coin so that with probability pheads occurs and with probability p tails occurs. Let X be the number of heads and Y be the number of tails. Prove X and Y are dependent (b) Now, toss the same coin n times, where n is a random integer with Poisson distribution: n~Poisson(A) Let X be the random variable counting the number of heads, Y the random variable counting the number of tails. Prove...
ASAP
Exercise 6. This problem describes an experiment in which conditional probabilities are used to compute "proper" probability. The experiment starts with two urns, Urn #1 contains 5 white marbles and 2 black marbles. Urn #2 contains 7 white marbles and 3 black marbles. One marble from each urn is drawn at random. (For each urn, the chance of each marble being drawn is the same.) Let T be the event that the two marbles are the same color. Let...
Answers for all questions please!!
8) A bag contains 10 red marbles and 8 green marbles. Anne picks 3 replacement, and observes the color of each marble. The number of green binomial random variable. If we let success correspond to getting success probability, p?What is the number of trials? marbles at random, with 8) marbles, X, is a a green marble, what is the A) P- n3 Solve the problem. 9) One hundred people were asked, "Do you favor the...
28. In many problems about modeling count data, it is found that values of zero in the data are far more common than can be explained well using a Poisson model (we can make P(X 0) large for X ~ Pois(A) by making λ small, but that also constrains the mean and variance of X to be small since both are X). The Zero-Inflated Poisson distribution is a modification of the Poisson to address this issue, making it easier to...
1. (6 pts) Consider a non-negative, discrete random variable X with codomain {0, 1, 2, 3, 4, 5, 6} and the following incomplete cumulative distribution function (c.d.f.): 0 0.1 1 0.2 2 ? 3 0.2 4 0.5 5 0.7 6 ? F(x) (a) Find the two missing values in the above table. (b) Let Y = (X2 + X)/2 be a new random variable defined in terms of X. Is Y a discrete or continuous random variable? Provide the probability...
Suppose we toss a coin (with P(H) p and P(T) 1-p-q) infinitely many times. Let Yi be the waiting time for the first head so (i-n)- (the first head occurs on the n-th toss) and Xn be the number of heads after n-tosses so (X·= k)-(there are k heads after n tosses of the coin). (a) Compute the P(Y> n) (b) Prove using the formula P(AnB) P(B) (c) What is the physical meaning of the formula you just proved?
Suppose...
3. An urn contains 2 black, 2 red, and 4 white marbles. You draw a marble at random. a) What is the sample space? b) What are all events (power Class)? c) What is the probability of each event? 4. A coin is tossed ten times and number of heads is noted. a) What is the probability that the number of heads is four? b) What is the probability of at least seven heads come? 6. X is a Binomial...
Exercise 8.26. Suppose I have an urn with 9 balls: 4 green, 3 yellow and 2 white ones. I draw a ball from the urn repeatedly with replacement. (a) Suppose I draw n times. Let X., be the number of times I saw a green ball followed by a yellow ball. Calculate the expectation Ex, (b) Let y be the number of times I drew a green ball before the first white draw. Calculate E[Y]. Can you give an intuitive...
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