Question

Construct the probability distribution of random variables then draw the corresponding histogram.

Three coins are tossed. Let x be the random variables representing the number of heads that occur. Find the values of the random variable Z.

Answer 1

Z ~ BIN(3, 0.5), so Z = {0, 1, 2, 3}

$P(Z=0)={3 \choose 0}*({\frac 1 2})^3={\frac 1 8}$

$P(Z=1)={3 \choose 1}*({\frac 1 2})^3={\frac 3 8}$

$P(Z=2)={3 \choose 2}*({\frac 1 2})^3={\frac 3 8}$

$P(Z=3)={3 \choose 3}*({\frac 1 2})^3={\frac 1 8}$