Question

In: Statistics and Probability

Assume that X has a Poisson distribution with mean of 3.7. Calculate the followings. P(X=1) P(1<X<4)...

Assume that X has a Poisson distribution with mean of 3.7. Calculate the followings.

  1. P(X=1)
  2. P(1<X<4)
  3. P(1<X<2)
  4. P(2<X<4)
  5. P(X=1.5)
  6. P(X=0)
  7. P(X<-2)
  8. Standard Deviation of X
  9. Mean of X

Solutions

Expert Solution


Related Solutions

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:...
Suppose that x has a Poisson distribution with μ = 22. (a) Compute the mean, μx,...
Suppose that x has a Poisson distribution with μ = 22. (a) Compute the mean, μx, variance, σ2xσx2, and standard deviation, σx. (Do not round your intermediate calculation. Round your final answer to 3 decimal places.)   µx = , σx2 = , σx = (b) Calculate the intervals [μx ± 2σx] and [μx ± 3σx ]. Find the probability that x will be inside each of these intervals. Hint: When calculating probability, round up the lower interval to next whole...
Let X be the amount of cash a consumer has. Given a Poisson distribution with mean...
Let X be the amount of cash a consumer has. Given a Poisson distribution with mean = $30. Lets say you have a producer who wants to sell $300 worth of stuff. What is the probability that 11 consumers exactly can buy that $300 worth of stuff.
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)=
Let X have a Poisson distribution with mean μ . Find E(X(X-1)) and use it to...
Let X have a Poisson distribution with mean μ . Find E(X(X-1)) and use it to prove that μ = σ 2 .
A geometric distribution has a pdf given by P(X=x) = p(1-p)^x, where x = 0, 1,...
A geometric distribution has a pdf given by P(X=x) = p(1-p)^x, where x = 0, 1, 2, ..., and 0 < p < 1. This form of the geometric starts at x = 0, not at x = 1. Given are the following properties: E(X) = (1-p)/p, and Var(X) = (1-p)/p^2 A random sample of size n is drawn; the data are X1, X2, ..., Xn. A. Derive the Fisher information function for the parameter p. B. Find the Cramér-Rao...
1. Assume that x has a normal distribution with the specified mean and standard deviation. Find...
1. Assume that x has a normal distribution with the specified mean and standard deviation. Find the indicated probability. (Round your answer to four decimal places.) μ = 6.0; σ = 1.1 P(7 ≤ x ≤ 9) = 2. Assume that x has a normal distribution with the specified mean and standard deviation. Find the indicated probability. (Round your answer to four decimal places.) μ = 51; σ = 16 P(40 ≤ x ≤ 47) =
1)Assume that x has a normal distribution with the specified mean and standard deviation. Find the...
1)Assume that x has a normal distribution with the specified mean and standard deviation. Find the indicated probability. (Round your answer to four decimal places.) μ = 4; σ = 6 P(1 ≤ x ≤ 13) = 2) Assume that x has a normal distribution with the specified mean and standard deviation. Find the indicated probability. (Round your answer to four decimal places.) μ = 2.7; σ = 0.39 P(x ≥ 2)
1. Assume that x has a normal distribution with the specified mean and standard deviation. Find...
1. Assume that x has a normal distribution with the specified mean and standard deviation. Find the indicated probability. mean=100, stadard dev. = 18 P(x> or = 120) = ? 2. Thickness measurements of anciwnt prehistoric Native American pot shards discovered in a Hopi village are approximately normally distributed, with a mean of 4.6 mm and a standard dev. of 1.5mm. For a randomly found shard, find the following probabilities. a) The thickness is less than 3.0mm b) The thickness...
Consider a Poisson distribution in which the offspring distribution is Poisson with mean 1.3. Compute the...
Consider a Poisson distribution in which the offspring distribution is Poisson with mean 1.3. Compute the (finite-time) extinction probabilities un = P{ Xn = 0 | X0 = 1 } for n = 0, 1, . . . , 5. Also compute the probability of ultimate extinction u∞.
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT