Question

Four coins are tossed. Let Z be the random variable representing the number of heads that occur. Find the values of the random variable Z. Construct a probability distribution and draw the corresponding histogram

Answer 1

Z ~ BIN(4, 0.5), so Z = {0, 1, 2, 3, 4}

$P(Z=0)={4 \choose 0}*({\frac 1 2})^4={\frac 1 {16}}$

$P(Z=1)={4 \choose 1}*({\frac 1 2})^4={\frac 4 {16}}={\frac 1 4}$

$P(Z=2)={4 \choose 2}*({\frac 1 2})^4={\frac 6 {16}}={\frac 3 8}$

$P(Z=3)={4 \choose 3}*({\frac 1 2})^4={\frac 4 {16}}={\frac 1 4}$

$P(Z=4)={4 \choose 4}*({\frac 1 2})^4={\frac 1 {16}}$