Question

2. X123456 Suppose that the random variable, X, is a number on the biased die and...

2. X123456

Suppose that the random variable, X, is a number on the biased die and the p.d.f. of X is as shown below;

            

P(X=x) 1/6 1/6 1/5 k

a) Find;

  1. (i) the value of k.

  2. (ii) E(X)

  3. (iii) E(X2)

  4. (iv) V ar(X)

  5. (v) P(1£X<5)

1/5 1/6

      

  1. b) If events A and B are such that they are independent, and P(A) = 0.3 with P(B) = 0.5;

    1. Find P(A n B) and P(AUB)

    2. Are A and B mutually exclusive? Explain.

  2. c) In how many ways can the letters of the word STATISTICS be arranged?

Math   Statistics-And-Probability   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1


  

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Two fair die are tossed, and the uppermost face of each die is observed. The following...
Two fair die are tossed, and the uppermost face of each die is observed. The following events are defined from this random experiment: AA represent the event the uppermost faces sum to five BB represent the event that the product of the uppermost faces is four. For example, die1*die2 = 4 CC represent the event that the absolute difference between the uppermost faces is 1. For example, |die1−die2|=1|die1−die2|=1 Part (a) Find the probability that the uppermost faces do not sum...
suppose events A and B are such that p(A)=0.25,P(B) =0.3 and P(B|A)= 0.5 i) compute P(AnB)...
suppose events A and B are such that p(A)=0.25,P(B) =0.3 and P(B|A)= 0.5 i) compute P(AnB) and P(AuB) ii) Are events A and B independent? iii) Are events A and B mutually exclusive? b)if P(A)=0.6, P(B)= 0.15 and P(B|A')=0.25, find the following probabilities I)P(B|A), P(A|B),P(AuB)
1. Given a discrete random variable, X , where the discrete probability distribution for X is...
1. Given a discrete random variable, X , where the discrete probability distribution for X is given on right, calculate E(X) X P(X) 0 0.1 1 0.1 2 0.1 3 0.4 4 0.1 5 0.2 2. Given a discrete random variable, X , where the discrete probability distribution for X is given on right, calculate the variance of X X P(X) 0 0.1 1 0.1 2 0.1 3 0.4 4 0.1 5 0.2 3. Given a discrete random variable, X...
QUESTION 1 You flip a coin and roll a 10 sided die. How many elements are...
QUESTION 1 You flip a coin and roll a 10 sided die. How many elements are in the sample space?   QUESTION 2 You flip a coin and roll a 10 sided die. What is the probability getting a tail and rolling a 5? QUESTION 3 How many ways can you select 2 items from 20 if order does not matter? QUESTION 4 How many ways can you select 2 items from 20 if order matters? QUESTION 5 Suppose that we...
A die is suspected of being biased. It is rolled 24 times with the following results:...
A die is suspected of being biased. It is rolled 24 times with the following results: Outcome 1 2 3 4 5 6 Total Outcome Probability 1/6 1/6 1/6 1/6 1/6 1/6 1 Expected Frequency A B C D E F 24 Observed Frequency 8 4 1 8 3 0 24 Conduct a significance test at a significant level of 5% to see if the die is biased. A die is not biased if the probability of each of the...
Let X be a random variable that takes on values between 0 and c. That is...
Let X be a random variable that takes on values between 0 and c. That is P{0 ≤ X ≤ c} = 1. Show that V ar(X) ≤ c2 4 Hint: One approach is to first argue that E[X2] < cE[X] and then use this fact to show that V ar(X) ≤ c2[α(1 − α)] where α = E[X]/c.
A die is suspected of being biased. It is rolled 24 times with the following results:...
A die is suspected of being biased. It is rolled 24 times with the following results: Outcome 1 2 3 4 5 6 Total Outcome Probability 1/6 1/6 1/6 1/6 1/6 1/6 1 Expected Frequency A B C D E F 24 Observed Frequency 8 4 1 8 3 0 24 1) Conduct a significance test at a significant level of 5% to see if the die is biased. A die is not biased if the probability of each of...
(a) TRUE / FALSE If X is a random variable, then (E[X])^2 ≤ E[X^2]. (b) TRUE...
(a) TRUE / FALSE If X is a random variable, then (E[X])^2 ≤ E[X^2]. (b) TRUE / FALSE If Cov(X,Y) = 0, then X and Y are independent. (c) TRUE / FALSE If P(A) = 0.5 and P(B) = 0.5, then P(AB) = 0.25. (d) TRUE / FALSE There exist events A,B with P(A)not equal to 0 and P(B)not equal to 0 for which A and B are both independent and mutually exclusive. (e) TRUE / FALSE Var(X+Y) = Var(X)...
Suppose that a random variable X has the distribution (pdf) f(x) =kx(1 -x^2) for 0 <...
Suppose that a random variable X has the distribution (pdf) f(x) =kx(1 -x^2) for 0 < x < 1 and zero elsewhere. a. Find k. b. Find P(X >0. 8) c. Find the mean of X. d. Find the standard deviation of X. 2. Assume that test scores for all students on a statistics test are normally distributed with mean 82 and standard deviation 7. a. Find the probability that a single student scores greater than 80. b. Find the...
A number x is selected at random in the interval [-1, 2]. Let the events A...
A number x is selected at random in the interval [-1, 2]. Let the events A = {x<0} and B = {|x-0.5|<0.5}, and C = {x >0.75} (a) Find the probabilities of A, B, AB and AC. (b) Find the probabilities of AuB, AuC and AuBuC by using the appropriate axioms or corollaries.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT