The Poisson distribution with parameter λ has the mass function defined by p(x) = λ x e −λ/x! if x is a nonnegative integer (and 0 otherwise). Find the probability it assigns to each of the following sets:
a. [0, 2)
b. (−∞,1]
c. (−∞,1.5]
d. (−∞, 2)
e. (−∞,2]
f. (0.5, ∞)
g. {0, 1, 2}
Find the CDF of the uniform distribution on (0,1).
a. [0, 2)
= P(X = 0) + P(X = 1)
=
b. (−∞,1]
=P(X = 0) + P(X = 1)
=
c. (−∞,1.5]
=P(X = 0) + P(X = 1)
=
d. (−∞, 2)
=P(X = 0) + P(X = 1)
=
e. (−∞,2]
=P(X = 0) + P(X = 1) + P(X = 2)
=
f. (0.5, ∞)
= 1 - P(X = 0)
g. {0, 1, 2}
=P(X = 0) + P(X = 1) + P(X = 2)
=
The Poisson distribution with parameter λ has the mass function defined by p(x) = λ x...
Recall that a discrete random variable X has Poisson
distribution with parameter λ if the probability mass function of
X
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