Consider tossing three wellmade coins The eight possible out

Consider tossing three well-made coins. The eight possible outcomes are

hhh,hht,hth,htt,thh,tht,tth,ttt

Define x as the random variable \"number of heads showiing when three coins are tossed.\"

Obtain the mean and the variance of x. Simulate tossing three fair coins 10thousand times. Compute simulated mean and variance of x. Are the simulated values within 2% of the theoretical answers?

Solution

mean E(X) = [ x_i * P(x_i) ]

0 · 1/ 8 + 1 · 3/ 8 + 2 · 3/ 8 + 3 . 1/ 8 = 12/ 8 = 3 /2

variance ² = { [ x_i - E(x) ]² * P(x_i) }

= (0-3/2)^2*1/8 + (1-3/2)^2*3/8 +(2-3/2)^2*3/8 +(3-3/2)^2*1/8

= 0.28125 + 0.09375 + 0.09375 + 0.28125

= 0.75