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- Solve (F,G,H,i) only Please!!!A is a standard normal random variable. If A=a, and B is a normal random variable with parameters (2a,1), i) What is the distribution of B? ii) Find E(B) and Var(B) iii) Assuming B= 1234, what is the distribution of A? iv) Given that B=1234, find E(X|B=1234) and Var(X|B=1234)23. A variable is described at N(5,9). This indicates normal distribution, with Mean= 5 and Variance = 9. b) a) What are the corresponding Z values for X values of 2 & 5? What is the probability that X is less than 2? What is the probability that X is less than 5? c) C: What is the probability that X is between 2 and 5? e) What is the probability that Z < -1.24? d)
- Suppose X is a random variable of uniform distribution between 1 and 7. Find E(X)If X is a normal random variable with mean μ = 3 and standard deviation σ = a. P(X > 11) b. P(2-3|X > -5) 4, findSuppose the random variable X follows a normal distribution with mean 80 and variance 100. Then the probability is 0.6826 that X is in the symmetric interval about the mean between two numbers are A) -2 to 2 B) -3 to 3 C) -1 to 1 D) none
- 13. A continuous random variable is uniformly distributed between 200 and 220. a. What is the probability a randomly selected value will be greater than 215? b. What is the probability a randomly selected value will be less than 205? c. What is the probability a randomly selected value will be between 205 and 215? a. P(x > 215) = (Simplify your answer.) b. P(x< 205) = (Simplify your answer.) c. P(205Find the mean of the given probability distribution. 16) In a certain town, 70% of adults have a college degree. The accompanying table describes th 16) probability distribution for the number of adults (among 4 randomly selected adults) who h college degree. P(x) X 0 0.0081 1 0.0756 2 0.2646 3 0.4116 4 0.240110. Two random variables X and Y take on the values i and 2 with probability 1/2' (i = 1,2, ...). Show that the probabilities sum to one. Find the expected value of X and Y.Let Y1, Y2, Y3 denote independent exponential random variables with respective rates A; for i e {1,2, 3}. Answer the following questions; (a) Compute E[Y1 +Y2 +Y3]Y1 > 1, Y2 > 2, Y3 > 3]. Your answer should be an expression using A;'s. (b) Compute the probability that Yı is the smallest among three random variables. Hint: P(X < Y) = S" Px,y (x, y)dædy where Px,Y (x, y) is the joint density function.If the number X of particles emitted during a 1-hour period from a radioactive source has a poisson distribution with parameter equal to 4 and that the probability that any emitted is recorded is p=0.9 find the probability distribution of the number Y of the particles recorded in a 1-hour and hence the probability that no particle is recordeda) Let X₁, X2, X3,..., X₁ be a random sample of size n from population X. Suppose that X follows an exponential distribution with parameter 0 and Y = ===1 X₁. n b) i) Show that y follows a chi-square distribution with 2n degrees of freedom. ii) What is the value of the sample size n, if P(Y > 20.4831) = 0.025? iii) What is the value of sample size n, if P(|Y - 2n| <40) ≥ 0.025? iv) Use the Central Limit Theorem to compute P(100 < Y < 115), for n = 40. Let X₁, X2, ..., X5 be a random sample of size 5 from the standard normally population. If the statistic Y is given by Y = X1 X2 X3 ₁²+X3² +X5² i) Briefly explain why Y follows a Student's t distribution with 3 degrees of freedom. ii) Compute the probability that Y is between 2.35 and 5.84. iii) What is the mean and variance of the statistic Y?SEE MORE QUESTIONS