(iii) Given that the events A and B are such that : 3 P(A) = P(AUB)= and P (B) = p. 2' Find the value of 'p' if the events are independent.
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- During his 4 years at college, Billy takes N exams, where N has a Poisson distribution with parameter 2. On each exam, the probability of getting an A is p, independently of any other exam. Let X be the number of |A's received on the N exams. What is the probability distribution of XỊN? Find the correlation coefficient between N and X as an expression in terms of p and/or 2.A report from the Department of Agriculture has shown that 35% of the produce in supermarkets has been genetically modified (labeled a GMO). A simple random sample of 12 different pieces of produce are selected. What is the probability that exactly 4 of the pieces of produce has been genetically modified (labeled a GMO)? Show how you calculated your result here (type in what you typed on your calculator or computer, the function used on the calculator/computer with value input, etc) Calculation: __________ Now type in your final simplified or rounded answer, if necessary round your answer to four decimal places. P(exactly 4 are GMO) =__________It's desired to model the random variable X with a shape that rises to a peak near x=6 and whose possible values are integers 1-6. Copy paste the following lines of code into R: x <- 1:10 shape <- x*(12-x) barplot(shape, names. arg=x) This "shape" isn't a valid PMF because the numbers don't sum to 1. Convert the numbers in "shape" to valid probabilities and report P(X-5). Copy/paste all digits from R into your answer here.
- The United States Department of Agriculture (USDA) found that the proportion of young adults ages 20–39 who regularly skip eating breakfast is 0.2380.238. Suppose that Lance, a nutritionist, surveys the dietary habits of a random sample of size ?=500n=500 of young adults ages 20–39 in the United States. Apply the central limit theorem to find the probability that the number of individuals, ?,X, in Lance's sample who regularly skip breakfast is greater than 126126. You may find table of critical values helpful. Express the result as a decimal precise to three places.The spinner is spun one time. Find the probabilities. P(A) = P(C) = %3D A A E P(BUC)= P(B©) = Sample Space: P(B U A)= P(B U A)C = %3D P(D^)= P(AN C)= Page B.Q3/B/ Consider two events A and B such that P(A) = and P(B) =, find the value of P(Bn A°) if 1) A and B disjoint 2) ACB.
- 2) The number x of people admitted to an intensive care unit in a particular hospital, on any given day, has a Poisson probability distribution with mean equal to five (5) people per day. What is the probability that the number of people admitted to an intensive care unit on a particular day is three (3)? Solve using Poisson's formula (Mendenhall et al., 2015).Consider three independent events, A1,A2,A3, and let Pi = P(Ai) for i = 1,2,3. Express the probability that at least one of these events occurs in terms of the pi’sWhat is the z-score of x = 3 if X ~ N(5,2)? -5 1
- Approximately 8% of students at a local high school participate in after-schoold sports every year of hs. A group of 60 seniors is randomly choosen. Of interest is the number who participated in after school aports every year of hs. In words define the variable X, list the values that x may take on, Write the distribution of X mathmatically with correct notation, how many seniors in this group are expected to have participated in after school sports every year of hs, Find the probability that no seniors participated in after school sports every year of hs- list the Excel command used, Based on numerical values would you be suprised if none of the seniors participated in after school sports every year of hs and why?please use the Statistical tables providedFind Var(X) if X is a Uniformly distributed b Binomially distributed c Normally distributed By Dr. S. O. Edeki Department of Mathematics, Covenant University, Nigeria.
