Consider the binomial distribution with n trials and P(S) = p(a) Show that _PLY) = n -y+ 1)P for y = 1, 2.Ply - 1)... n. Equivalently, for y = 1, 2, .., n, the equation p(y) = -y + 1)P p(y - 1) gives a recursive relationship between the probabilities associated with successive values of Y.yaygPly - 1)(,": Jo - - ( - 1)- n- y+ 1)pya(b) Ifn = 70 and p = 0.04, use the above relationship to find P(Y < 3). (Round your answer to four decimal places.)(c) Show that – P = -Y* L)P > 1 if y < (n + 1)p. This establishes that p(y) > P(v - 1) if y is small (y < (n + 1)p) and ply) < p(y - 1) if y is large (y > (n + 1) p). Thus, successive binomial probabilities increase for a while and decrease from then on.Ply - 1)(n + 1)p > yyq(n +1- y)p > y+(n +1- y)p >(n +1- y)p> 1yqShow that PV) <1 if y > (n + 1) p.Ply -(n + 1)p < y(n +1- y)p « y -(n +1- y)p <(n +1- y)e < 1yqShow that PL = 1 if (n + 1)p is an integer and y = (n + 1)p.Ply - 1)(n + 1)p = y(n +1- y)p = y +(n +1- y)p =(n +1- yle = 1ya

a)Given binomial distribution Y with parameters n,p The binomial probability distribution function…

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A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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1.If the cosmic radiation to which a person is exposed while flying by jet across US is a random variable having mean 4.35 mrem and standard deviation 0.59 mrem,find the probabilities that the amount of cosmic radiation to which a person will be exposed on such a flight is (a)Between 4.00 and 5.00 mrem (b)At least 5.50 mrem (c)Less than 4.00 mrem
3.3
12. Suppose (1, 2, ..., n) is a random sample from ...,n) is a random sample from a normal distribution, find the absolute efficiency of the maximum likelihood estimator of 0 if, x; ~ ~ N(0, 1).
A binomial experiment for the random variable X was performed with 10 trials. The probability of success was found to 0.44. Determine the following probabilities: [Round to four decimal places.] a.) P(X = 4)= b.) P(X 6) =
Suppose the number of radios in a household has a binomial distribution - with parameters n Find the probability 10, and p = 20 %. of a household having: (a) 6 or 8 radios (b) 6 or fewer radios (c) 6 or more radios (d) fewer than 8 radios. (e) more than 6 radios
An experiment can result in one of five equally likely simple events, E₁, E₂, A: E₂, E4 2' P(A) = = 0.4 B: E₁, E3, E4, E5 P(B) = 0.8 C: E₂, E3 Refer to the following probabilities. P(A n B) = 0.2 P(AIB) = 0.25 P(BIA) P(BU C) = 1 P(BIC) 0.5 P(CIB) 0.25 Use the Addition and Multiplication Rules to find the following probabilities. (a) P(AUB) (b) P(An B) = 0.5 P(A U B) = ---Select--- + ---Select--- ✓ P(A n B) = ---Select--- (c) P(B n C) Yes P(B n C) = ---Select--- No P(C) = 0.4 . P(B) = = P(C) = = ---Select--- V = Do the results agree with those obtained by listing the simple events in each? P(A U B) = P({E₁, E₂, E3, E4, E5}) = 1 P(A n B) = P({E₁}) = 0.2 P(B n C) = P({E3}) = 0.2 .., E5. Events A, B, and C are defined as follows.
23. *An insurance policy pays an individual 100 per day for up to 3 days of hospitalization and 25 per day for each day of hospitalization thereafter. The number of days of hospitalization, X, is a discrete random variable with probability function Pr(X = k) = (1/15)(6 – k), k = 1, 2, 3, 4, 5. Calculate the expected payment for hospitalization under this policy. (213.3)
6) Approximate the following binomial probabilities by the use of normal approximation.a.P(x< 12, n = 50, p = 0.3)b.P(12 <x< 18, n = 50, p = 0.3
2. Let x be a binomial random variable with n=20 and p=.3. Which of the following gives p(x = 13)? • (a) Use binomial table for n=20, p=0.3, and k = 13 • (b) Use binomial table for n=20, p=0.3, and k = 12 • (c) Subtract (b) from (a), i.e. p(x= 13) = p(x ≤ 13) – p(x ≤ 12) PLEASE SHOW ME HOW TO DO IT SO I CAN LEARN IT?
Let S be a sample space and E and F be events associated with S. Suppose that Pr(E) = 0.5, Pr(F) = 0.3 and Pr(ENF) = 0.2. Calculate the following probabilities. (a) Pr(E|F) (b) Pr(F|E) (c) Pr(티F') (d) Pr (E'JF') ... (a) To find Pr(E|F), simplify the fraction with Pr(EnF) in the numerator and Pr(F) in the denominator. Pr(E|F) = || |(Type an integer or a simplified fraction.)
Which one of the following is not a true for the Negative Binomial distribution ? a) The random variable can start at y =0 b) The trials in the experiment are independent c) The negative binomial distribution parameters are the number of successes and the probability of a success d) The random variable denotes the number of failures that occured until the rth success is obtained e) There are only two outcomes, a success and a failure
1- The level of income depends on famer work and it varied according to the rate of rainfall, the following table showing two alternatives of the agricultural work, determine the level of the risk from each alternative by: a- using the expected value method, b- using the standard deviation c- using Coefficient of variation method, and for each one show which alternative will you choose? Table: Farmer income at different level of rainfall and with different probabilities State Income (JD/Year) (Rainfall rate) Alternative A Alternative B Prob. Income Prob. Income High 0.2 30000 0.2 50000 Moderate 0.5 25000 0.5 25000 Low 0.3 20000 0.3

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