Consider a binomial experiment with n = 20 and p = 0.70. a. Compute f(12) (to 4 decimals). b. Compute f(16) (to 4 decimals). c. Compute P(x > 16) (to 4 decimals). d. Compute P(x ≤15) (to 4 decimals). e. Compute E(x). f. Compute Var(x) (to 1 decimal) and σ (to 2 decimals). Var(x) = σ =
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- Suppose the probability of erroneously transmitting a single digit is P=0.03. Compute the probability of transmitting a 4-bit code word with (a) at most one error, and (b) exactly four errors.There is a chance that a bit transmitted through a digital transmission channel is received in error. Let X equal the number of bits in error in the next four bits transmitted. The possible values of X are {0,1,2,3}. Suppose that P(X=0)=0.6, P(X=1)= 0.3, P(X=2)= 0.05, P(X=3)= 0.05 What is the CDF of X at 3? i.e., what is F(3)? a). 0.6 b). 0.9 c). 0.95 d). 1 e). none of above For the random variable defined in question 12, if we know that Var(X)=0.6475, what is the standard deviation of X? a). 0.55 b). 0.6475 c). 0.419 d). 0.8 e). none of aboveThe Math coordinator at Houston Community College collected the following data from first and second year students enrolled in the department's Spring classes. Any given student could only have been enrolled in one course. MATH 1324 (X) MATH 1314 (Y) MATH 1332 (Z) Total First year (A) Second year (B) 33 (d) Compute P(X U A). 152/209 X 42 (e) Compute P(Y n BC). 82/209 X 25 100 19 40 50 109 Total 52 82 75 All answers to the following questions should be exact. (a) If a student is selected at random, what is the probability the student is a first year or a second year student? 209/209 209 (b) If a student is selected at random, what is the probability the student is not taking MATH 1324 and is not taking MATH 1332? 82/209 (c) If a student is selected at random, what is the probability the student is not taking MATH 1324 or is not taking MATH 1332? 127/209 X
- 4(a). A fair four-sided die has the numbers 1, 2, 3 and 4 respectively on the four faces. Find the mean and variance of the number to turn “face up" on any one roll of the die. 4(b). Suppose that the four-sided die in part (a) of this question is to be rolled twice. Define T2 as the sum of the two numbers that will turn up. Use whatever method you like to find the mean and variance of T2.For Numbers 4 and 5: Dr. Kae Dee, a resident cardiologist who intends to specialize in vascular medicine, wants to verify a claim from a study which states that chronic venous insufficiency affects about 1 in 20 adults. She obtained records from 40 randomly selected hospitals from municipalities with relatively similar population sizes and obtained the number of reported chronic venous insufficiency cases. Let X be the number of reported chronic venous insufficiency cases. 4. Which of the following is(are) TRUE? 1. X is a discrete random variable with possible values x = {0, 1, 2, 3, ..., 40) II. The sum of probabilities of all values of X is 1. A. I only 5. Presented below is the probability distribution table from Dr. Kae Dee's study. X=x P[X=x] A. 1.00 B. II only 19 0.22 20 0.38 B. 4.10 C. Both I and II 21 0.11 The expected number reported chronic venous insufficiency cases is 22 C. 20.57 D. Neither I nor II 23 0.10 on the average. D. 105How were the correct answers of 0.2241 and 0.1792 attained?
- . Suppose X ~ N(2,3). What value of x has a z-score of -0.67?9. (a) Show that if n is an integer, then: 3 () = 4". %3D (b) Let n be a positive integer. Show that ()+ () = ). n+11a) Use Matlab to compute and simulate the roots of the following function;(i) 5x4+21x2−14x+30=0(ii) x4−4=0 b). It is known that only 60% of a defected computer can berepaired. A sample of 8 computers is selected randomly, findthe probability that;(i) At most 3 computers can be repaired.(ii) 5 or less can be repaired(iii) None can be repairedBased on your output for these, how will you have advised after a critical analysis from your output.
- Assume that W (t) is a standard Brownian motion and that S(t) is a random variable defined as S(t) = 8 · 2W(t). Determine§5. (8 p) Let (4A)¯¹= ( 2/3 2). Get At.Solve the following problems by using the binomial formula.a. If n = 4 and p = 0.50, find P(x = 3).b. If n = 7 and p = 0.70, find P(x = 4).c. If n = 10 and p = 0.60, find P(x ≥ 7).d. If n = 12 and p = 0.45, find P(5 ≤ x ≤ 7). Appendix A Statistical Tables (Round the intermediate values to 4 decimal places. Round your answers to 4 decimal places, e.g. 0.2153.)a. P(x = 3) = enter probability rounded to 4 decimal places b. P(x = 4) = enter probability rounded to 4 decimal places c. P(x ≥ 7) = enter probability rounded to 4 decimal places d. P(5 ≤ x ≤ 7) = enter probability rounded to 4 decimal places