Question
In: Math
show that standardized poisson follows poisson with mean 0 and variance 1
show that standardized poisson follows poisson with mean 0 and variance 1
Solutions
Expert Solution
Let X have a Poisson distribution with parameter λ.
Then it can be shown that the random variable
Y = (X - n)/√(n)
where n is the parameter of the Poisson distribution.
will converge to a standard normal distribution as λ goes to infinity. which is nothing but standard Normal Distribution with Mean 0 and Variance 1.
which is the Moment Generating Function of Standard Normal Distribution with mean zero and variance 1.
milcah answered 3 months agoRelated Solutions
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c. What is the value of Z if only 6.5% of all possible Z values are larger?
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b. The probability that Z is greater than 1.81 is________
c. The probability that Z is between -1.59 and 1.81 is______
d. The probability that Z is less than -1.59 or greater than
1.81______
given a standardized normal distribution (with a mean of 0 and a standard deviation of 1)...
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b. P(Z < -0.23)
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D. what is the value of Z if only 11.51% of all
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