CSCI-270 probability and statistics for computerHomework Answers
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CSCI-270 probability and statistics for computer
Consider the sample space of outcomes of two throws of...
This is discrete mathematics If you do it right, I must give praise. You must use probability spa...
This is discrete mathematics
If you do it right, I must give praise.
You must
use probability space is a triple relative
acknowledge.
S: is a
sample sapce
E=p(s) is
the set of all events
P:
E-->R is a function.
The important thing that I need to say three times:
If you don't know how to do it, please don't do
it.
don't copy others,
especially for question (a), give sample space, probability
measure
The important thing that I need...
3 Probability and Statistics [10 pts] Consider a sample of data S obtained by flipping a...
3 Probability and Statistics [10 pts] Consider a sample of data S obtained by flipping a coin five times. X,,i e..,5) is a random variable that takes a value 0 when the outcome of coin flip i turned up heads, and 1 when it turned up tails. Assume that the outcome of each of the flips does not depend on the outcomes of any of the other flips. The sample obtained S - (Xi, X2,X3, X, Xs) (1, 1,0,1,0 (a)...
Exercise 1.9. Consider the sample space SB from Exercise 1.3, with probabil- ity distribution as defined...
Exercise 1.9. Consider the sample space SB from Exercise 1.3, with probabil- ity distribution as defined in Table 1.15. Recast the sample space as variables. What is the probability distribution for each variable? Exercise 1.3. Consider the experiment of flipping a fair coin, and if it lands heads, rolling a fair four-sided die, and if it lands tails, rolling a fair six-sided die. Suppose that we are interested only in the number rolled by the die, and a sample space...
a fair coin is tossed three times. A. give the sample space B. find the probability...
a fair coin is tossed three times. A. give the sample space B. find the probability exactly two heads are tossed C. Find the probability all three tosses are heads given that the last toss is heads
The next four questions (5 to 8) refer to the following: An unfair coin is tossed...
The next four questions (5 to 8) refer to the following: An unfair coin is tossed three times. For each toss, the probability that the coin comes up heads is 0.6 and the probability that the coin comes up tails is 0.4. If we let X be the number of coin tosses that come up heads, observe that the possible values of Xare 0, 1, 2, and 3. Find the probability distribution of X. Hint: the problem can be solved...
Construct a sample space (list or make a tree diagram of all of the outcomes) for...
Construct a sample space (list or make a tree diagram of all of the outcomes) for the experiment of a) rolling a 12 sided die and flipping a coin at the same time. Assuming each outcome is equally likely, what is the probability of: DO NOT REDUCE b) rolling a number less than 4 and getting heads? c) rolling an odd number and getting tails? d) rolling a 7 and getting ( heads or tails)
Problem 4 (Poisson Distributed RV) In a composite experiment, Z is a Poisson-distributed RV with ...
Problem 4 (Poisson Distributed RV) In a composite experiment, Z is a Poisson-distributed RV with parameter A, i.e P(Z k, and a coin with probability p of showing heads is tossed Z times (after observing Z). Let X denote the number of heads and Y denote the number of tails after Z tosses (a) Clearly specify the sample space 2xy, the set of values taken jointly by X and Y. (b) Determine the joint pmf of X and Y (in...
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...
If the coin is unbalanced and a head has a 30% chance of occurring, find the joint probability distribution f(w, z)
A coin is tossed twice. Let Z denote the number of heads on the first toss and let W denote the total number of heads on the two tosses. If the coin is unbalanced and a head has a 30% chance of occurring, find the joint probability distribution f(w, z)
You toss a penny and observe whether it lands heads up or tails up. Suppose the...
You toss a penny and observe whether it lands heads up or tails up. Suppose the penny is fair, i.e., the probability of heads is 1/2 and the probability of tails is y. This means every occurrence of a head must be balanced by a tail in one of the next two or three tosses. if I flip the coin many, many times, the proportion of heads will be approximately %, and this proportion will tend to get closer and...
This is discrete mathematics
If you do it right, I must give praise.
You must
use probability space is a triple relative
acknowledge.
S: is a
sample sapce
E=p(s) is
the set of all events
P:
E-->R is a function.
The important thing that I need to say three times:
If you don't know how to do it, please don't do
it.
don't copy others,
especially for question (a), give sample space, probability
measure
The important thing that I need...
3 Probability and Statistics [10 pts] Consider a sample of data S obtained by flipping a coin five times. X,,i e..,5) is a random variable that takes a value 0 when the outcome of coin flip i turned up heads, and 1 when it turned up tails. Assume that the outcome of each of the flips does not depend on the outcomes of any of the other flips. The sample obtained S - (Xi, X2,X3, X, Xs) (1, 1,0,1,0 (a)...
Exercise 1.9. Consider the sample space SB from Exercise 1.3, with probabil- ity distribution as defined in Table 1.15. Recast the sample space as variables. What is the probability distribution for each variable? Exercise 1.3. Consider the experiment of flipping a fair coin, and if it lands heads, rolling a fair four-sided die, and if it lands tails, rolling a fair six-sided die. Suppose that we are interested only in the number rolled by the die, and a sample space...
The next four questions (5 to 8) refer to the following: An unfair coin is tossed three times. For each toss, the probability that the coin comes up heads is 0.6 and the probability that the coin comes up tails is 0.4. If we let X be the number of coin tosses that come up heads, observe that the possible values of Xare 0, 1, 2, and 3. Find the probability distribution of X. Hint: the problem can be solved...
Problem 4 (Poisson Distributed RV) In a composite experiment, Z is a Poisson-distributed RV with parameter A, i.e P(Z k, and a coin with probability p of showing heads is tossed Z times (after observing Z). Let X denote the number of heads and Y denote the number of tails after Z tosses (a) Clearly specify the sample space 2xy, the set of values taken jointly by X and Y. (b) Determine the joint pmf of X and Y (in...
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...
You toss a penny and observe whether it lands heads up or tails up. Suppose the penny is fair, i.e., the probability of heads is 1/2 and the probability of tails is y. This means every occurrence of a head must be balanced by a tail in one of the next two or three tosses. if I flip the coin many, many times, the proportion of heads will be approximately %, and this proportion will tend to get closer and...
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