Question

In: Math

Given that xx is a random variable having a Poisson distribution, compute the following: (a) P(x=1)P(x=1) when...

Given that xx is a random variable having a Poisson distribution, compute the following:

(a) P(x=1)P(x=1) when μ=4.5μ=4.5
P(x)=P(x)=

(b) P(x≤8)P(x≤8)when μ=0.5μ=0.5
P(x)=P(x)=

(c) P(x>7)P(x>7) when μ=4μ=4
P(x)=P(x)=

(d) P(x<1)P(x<1) when μ=1μ=1
P(x)=P(x)=

Expert Solution

Part a)

Probability mass function of Poisson distribution is

Part b)

P ( X <= 8 ) = 1

Part c)

P ( X > 7 ) = 1 - P ( X <= 6 ) = 1 - 0.8894

P ( X > 7 ) = 0.1106

Part d)

P ( X < 1 ) = P ( X = 0 ) = 0.3679

milcah answered 1 year ago

1 point) If xx is a binomial random variable, compute P(x)P(x) for each of the following...

1 point) If xx is a binomial random variable, compute P(x)P(x) for each of the following cases: (a) P(x≤1),n=5,p=0.3P(x≤1),n=5,p=0.3 P(x)=P(x)= (b) P(x>3),n=4,p=0.1P(x>3),n=4,p=0.1 P(x)=P(x)= (c) P(x<3),n=7,p=0.7P(x<3),n=7,p=0.7 P(x)=P(x)=

Question 1: Given the following probability distribution for a random variable X: x P(X=x) -2 0.30...

Question 1: Given the following probability distribution for a random variable X: x P(X=x) -2 0.30 -1 0.15 0 0.20 1 0.20 2 0.15 a) Explain two reasons why the above distribution is a valid probability distribution. b) Calculate μX and σX. c) Determine the cdf(X), and write it as an additional column in the table. d) Calculate P(−1<X≤3) . e) Draw a histogram that represents the probability distribution of X.

X is a random variable following Poisson distribution. X1 is an observation (random sample point) of...

X is a random variable following Poisson distribution. X1 is an observation (random sample point) of X. (1.1) Please find probability distribution of X and X1. Make sure to define related parameter properly. (1.2) Please give the probability distribution of a random sample with sample size of n that consists of X1, X2, ..., Xn as its observations. (1.3) Please give an approximate distribution of the sample mean in question 1.2(say, called Y) when sample size is 100 with detailed...

The demand for a replacement part is a random variable having a Poisson probability distribution with...

The demand for a replacement part is a random variable having a Poisson probability distribution with a mean of 4.7. If there are 6 replacement parts in stock, what is the probability of a stock-out (i.e., demand exceeding quantity on hand)?

Given a random variable XX following normal distribution with mean of -3 and standard deviation of...

Given a random variable XX following normal distribution with mean of -3 and standard deviation of 4. Then random variable Y=0.4X+5Y=0.4X+5 is also normal. (1)(2pts) Find the distribution of YY, i.e. μY,σY.μY,σY. (2)(3pts) Find the probabilities P(−4<X<0),P(−1<Y<0).P(−4<X<0),P(−1<Y<0). (3)(3pts) Find the probabilities P(−4<X¯<0),P(3<Y¯<4).P(−4<X¯<0),P(3<Y¯<4). (4)(4pts) Find the 53th percentile of the distribution of X.

If x is a binomial random variable, compute P(x) for each of the following cases:

If x is a binomial random variable, compute P(x) for each of the following cases: (a) P(x≤5),n=7,p=0.3 P(x)= (b) P(x>6),n=9,p=0.2 P(x)= (c) P(x<6),n=8,p=0.1 P(x)= (d) P(x≥5),n=9,p=0.3 P(x)=

If x is a binomial random variable, compute p(x) for each of the following cases: (a)...

If x is a binomial random variable, compute p(x) for each of the following cases: (a) n=3,x=2,p=0.9 p(x)= (b) n=6,x=5,p=0.5 p(x)= (c) n=3,x=3,p=0.2 p(x)= (d) n=3,x=0,p=0.7 p(x)=

1. If the random variable x has a Poisson Distribution with mean μ = 53.4, find...

1. If the random variable x has a Poisson Distribution with mean μ = 53.4, find the maximum usual value for x. Round your answer to two decimal places. 2. In one town, the number of burglaries in a week has a Poisson distribution with mean μ = 7.2. Let variable x denote the number of burglaries in this town in a randomly selected month. Find the smallest usual value for x. Round your answer to three decimal places. (HINT:...

If x is a binomial random variable, compute P(x) for each of the following cases, rounded...

If x is a binomial random variable, compute P(x) for each of the following cases, rounded to two decimal places: c) P(x<1),n=5,p=0.1 d) P(x≥3),n=4,p=0.5

A probability distribution function P(x) for a random variable X is defined by P(x) = P...

A probability distribution function P(x) for a random variable X is defined by P(x) = P r{X ≤ x}. Suppose that we draw a list of n random variables X1, X2, X3 · · · Xn from a continuous probability distribution function P that is computable in O(1) time. Give an algorithm that sorts these numbers in linear average case time.