If X ~ N(50; 100); Determine the value of '' k '' for both situation:
a) P(1, 16 < Z < k) = 9, 5%;
b) P(X < k) = 0, 0526.
If X ~ N(50; 100); Determine the value of '' k '' for both situation: a)...
(5) Recall that X ~Uniform(10, 1,2,... ,n - 1)) if if k E (0, 1,2,... ,n -1, P(x k)0 otherwise (a) Determine the MGF of such a random variable. (b) Let X1, X2, X3 be independent random variables with X1 Uniform(10,1)) X2 ~Uniform(f0, 1,2]) Xs~ Uniform(10, 1,2,3,4]). X3 ~ U x2 ~ Uniform(10, 1,2)) 13Uniform Find the laws of both Y1 X1 +2X2 +6X3 and Y2 15X1 +5X2 + X3. (c) What is the correlation coefficient of Yi and ½?...
(b) For n = 100, give an approximaation for P(Y> 100) (c) Let X be the sample mean, then approximate P(1.1< 1.2) for -100. 2. Consider a random sample XX from CDF F(a) 1-1/ for z [1, 0o) and zero otherwise. (a) Find the limiting distribution of XiI.n, the smallest order statistic. (b) Find the limiting distribution of XI (c) Find the limiting distribution of n In X1:m- 3. Suppose that X,,, are iid. N(0,o2). Find a function of T(x)x...
Determine the value of k that gives the appropriate probability. P( -k < Z < k ) = 0.246 P( 0 < Z < k ) = 0.324
16 pts) #4. TRUE/FALSE. Determine the truth value of each sentence (no explanation required). ________(a) A statement is a sentence that is true. ________(b) In logic, p q refers to the "inclusive or, " true when either p or q or both are true. ________(c) The phrase "not p and not q" means "not both p and q." ________(d) The conditional statement p q is true if p is false. ________(e) The negation of p q is p ~q. #5....
only number 5 5. The value of p, in silicon at T = 300 K is 105 cm. Determine (a) E.- E, and (b) n.. 5. The value of p, in silicon at T = 300 K is 10 cm. Determine (a) E-E, and (b) n.. 6. Consider a germanium semiconductor at T = 300 K. Calculate the thermal equilibrium concentrations of n, and p. for (a) N. = 10 cm", N. = 0, and (b) N. = 5 x...
2:50 PM Sun May 12 89%- X 2012 Spring All Exams.pdf 5. (30 pts) A unity feedback system has the loop transfer function shown below. a) Draw the complete Nyquist HG(s)-plane plot for both small K and large K. Use the Nyquist Path which encloses the pole of HG(s) that is at the origin. No other path will be accepted. b) Determine whether the closed loop system is stable for both small K and large Argue in terms of the...
6. A consumer with an income of $100 faces a situation where both good x and good y have the same price and are available in continuous quantities. In this situation, the person chooses 20 units of good x and 30 units of good y. Which of the following must be true? 1. There is something wrong because (20, 30) must be inside the budge line II. The MRS at (20,30) is 2/3 III. The consumer prefers (20, 30) to...
Find the sample proportions and test statistic for equal proportions. 100, X, = 36. n. 100. 05. two-tailed test. (Round your answers to 4 (a-1) Dissatisfied workers in two companies: X, 46, n, decimal places. Use Excel to calculate the p-value.) Heale p-value a/2 (a-2) Choose the appropriate hypotheses a. Ho:77 - - Ovs. Hy: -1 0. Reject Ho if Zeale < -1.96 or cale > 1.96 b. Hein - 1 Ovs. Hy:n - 1 0. Reject Ho if Zeale...
k=0 Q3 Suppose X has Poisson(1) distrubution. Calculate the following (a) Determine P(X = k) for k E No = {0, 1, 2, ..., n, ...}. [1] (b) Evaluate Ź P(X = k). [1] (c) Determine E(X). [1] (d) Determine E(X(X – 1)). [2] (e) Use the result in (d) to calculate E(X). [1] (f) Calculate Var(X). [1] (g) Calculate Eſax). [3] (h) Calculate Var(a*). [3] (i) Determine E (1+x). [2]
Problem 2 Statement: We know that the binomial series k k(k-1) k1 2)(k -n+1 n=0 converges for l < 1. (a) Use the binomial series to find the Taylor series for f(x)Va centered at z 16. What is the radius 16+ ( 16). of convergence R for your Taylor series? Hint: Problem 2 Statement: We know that the binomial series k k(k-1) k1 2)(k -n+1 n=0 converges for l