Let X ~ Poisson(4). Find

a. P(X = 1)

b. P(X = 0)

c. P(X<2)

d. P(X > 1)

e. μX

f. σX

Step 1 of 7</p>

Here we have to find the poisson probabilities

The pmf of Poisson distribution is p(x)=,x=0,1,2,............

Here Xpoisson()

Given Xpoisson(4)

So =4

Step 2 of 7</p>

a) Given P(X=1)=

=0.0733

Hence P(X=1)=0.0733

Step 3 of 7</p>

b) Given P(X=1)=

=0.0183

Hence P(X=1)=0.0183

Step 4 of 7</p>

c) given P(X<2)=P(0)+P(1)

=0.0733+0.0183

=0.0916

Hence P(X<2)=0.0916