Question

Let X∼Bernoulli(0.3) and Y∼Bernoulli(0.5) be independent. Define Z=X+Y−XY, find the distribution of Z.
a. Z∼Bernoulli(0.35)
b. Z~Bernoulli(0.65)
c. Z~Bernoulli(0.15)
d. Z~Bernoulli(.0.85)

Answer 1

Answer:

a. Z∼Bernoulli(0.35)

Step-by-step explanation:

Answer 2

Given:

Let X∼Bernoulli(0.3) , Y∼Bernoulli(0.5) and Z=?

Step-by-step explanation:

the given equation value,

$Z=X+Y-XY$

Step 1;Add the x and y ,

$X+Y$=Bernoulli(0.3) $+$ Bernoulli(0.5)

$X+Y$=Bernoulli(0.8)

Step 2;Multiply the x and y,

$XY$=Bernoulli(0.3) × Bernoulli(0.5)

$XY$=Bernoulli(0.15)

Step 3;Subtract Step 1 and Step 2 is equal to z

$Z$=Bernoulli(0.8) - Bernoulli(0.15)

$Z$=Bernoulli(0.65)

the value of z is b.Z~Bernoulli(0.65).