Performance Task – Statistics and Probability
1. A researcher surveyed the households in a remote area. The random variable X
represents the number of high school graduates in the households. The probability
distribution of X is shown below.
x
0
1
2
3
4
P(x)
0.02
0.18
0.30
0.40
0.10
Solution:
X
P(x)
X * P(x)
0
0.02
0
1
0.18
0.18
2
0.30
0.6
3
0.40
1.2
4
0.10
0.4
E[X] = ∑x * P(x)
E[X] = 0 + 0.18 + 0.6 + 1.2 + 0.4
E[X] = 2.38
The average household has 2.38 high school graduates.
2. You play a game of tossing an unbiased coin. On each toss if head appears, you win
55php. However, if a tail appears you lose 45php. If you continue to play the game, how
much do you expect to win or lose in the game?
Solution:
P(Head) = 0.5
P(Tail) = 0.5
E[X] = ∑x * P(x)
E[X] = 55 * 0.5 = 27.5
E[X] = -45 * 0.5 = -22.5
E[X] = 27.5 + (-22.5) = 5
Expect to win 5php if you continue to play the game.
