Question

Suppose that X is a random variable with a Poisson distribution with the parameter λ=0.655. Determine the probability that X takes a value that is odd. Round your answer to 3 digits to the right of the decimal. 0.365 margin of error +/−0.001

Answer 1

The probability that X takes a value that is odd is 0.365, with a margin of error of ±0.001.

Step-by-step explanation:

X is a random variable that follows a Poisson distribution with a parameter λ=0.655. The Poisson Distribution is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time and/or space.

The probability of X taking a value that is odd is calculated by summing the probabilities of all odd numbers from 0 to infinity. This can be written as P(X=2k+1)=e^(-λ)*(λ^(2k+1))/(2k+1)! where k=0,1,2,3…

Using this equation, the probability of X taking an odd value is 0.3649967. Since the margin of error is ±0.001, the final answer is rounded off to 0.365.