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Kelston Boys High School Mathematics Department
Homework/Assignment
Expected Value
US5258
Use expected values to solve problems
Year 13 2012
1
0.15
𝑥
𝑃(𝑋 = 𝑥)
1.
2.
3.
4.
-2
0.25
𝑃(𝑋 = 𝑥)
𝑃(𝑋 = 𝑥)
𝑃(𝑋 = 𝑥)
-4
0.28
0
0.44
2
0.23
18
0.05
1
0.41
3
0.12
5
0.12
7
0.35
Find the mean value of X.
Calculate the variance of X.
Calculate the expected value of the random variable 𝑌 = 50𝑥 + 8.
Calculate the variance of the random variable 𝑌 = 50𝑥 + 8.
𝑥
𝑃(𝑋 = 𝑥)
1.
2.
3.
4.
8
0.35
Find the mean value of X.
Calculate the variance of X.
Calculate the expected value of the random variable 𝑌 = 150𝑥 + 15.
Calculate the variance of the random variable 𝑌 = 150𝑥 + 15.
𝑥
1.
2.
3.
4.
5
0.40
Find the mean value of X.
Calculate the variance of X.
Calculate the expected value of the random variable 𝑌 = 200𝑥 + 30.
Calculate the variance of the random variable 𝑌 = 200𝑥 + 30.
𝑥
1.
2.
3.
4.
6
0.35
Find the mean value of X.
Calculate the variance of X.
Calculate the expected value of the random variable 𝑌 = 10𝑥 + 3.
Calculate the variance of the random variable 𝑌 = 10𝑥 + 3.
𝑥
1.
2.
3.
4.
3
0.50
-1
0.45
3
0.31
5
0.22
11
0.02
Find the mean value of X.
Calculate the variance of X.
Calculate the expected value of the random variable 𝑌 = 50𝑥 + 10.
Calculate the variance of the random variable 𝑌 = 50𝑥 + 10.
𝑥
𝑃(𝑋 = 𝑥)
1.
2.
3.
4.
-10
0.25
0
¼
𝑃(𝑋 = 𝑥)
8
¼
11
¼
6
¼
9
1/8
12
1/8
Find the mean value of X.
Calculate the variance of X.
Calculate the expected value of the random variable 𝑌 = 9𝑥 + 1.
Calculate the variance of the random variable 𝑌 = 9𝑥 + 1.
𝑥
𝑃(𝑋 = 𝑥)
-6
0.2
-1
0.2
0
0.2
1
0.2
6
0.2
Find the mean value of X.
Calculate the variance of X.
Calculate the expected value of the random variable 𝑌 = 18𝑥 + 2.
Calculate the variance of the random variable 𝑌 = 18𝑥 + 2
𝑥
𝑃(𝑋 = 𝑥)
1.
2.
3.
4.
5
¼
3
½
𝑃(𝑋 = 𝑥)
1.
2.
3.
4.
15
0.25
Find the mean value of X.
Calculate the variance of X.
Calculate the expected value of the random variable 𝑌 = 2𝑥 + 3.
Calculate the variance of the random variable 𝑌 = 2𝑥 + 3.
𝑥
1.
2.
3.
4.
5
0.25
Find the mean value of X.
Calculate the variance of X.
Calculate the expected value of the random variable 𝑌 = 24𝑥 + 3.
Calculate the variance of the random variable 𝑌 = 24𝑥 + 3.
𝑥
1.
2.
3.
4.
0
0.25
-8
0.3
6
0.3
15
0.2
31
0.1
50
0.1
Find the mean value of X.
Calculate the variance of X.
Calculate the expected value of the random variable 𝑌 = 1.8𝑥 + 0.5.
Calculate the variance of the random variable 𝑌 = 1.8𝑥 + 0.5
Practice Assessment1. The probability of getting a certain amount of points from a scoring
play over a rugby season is shown below.
2
0.15
𝑥
𝑃(𝑋 = 𝑥)
a.
b.
c.
d.
3
0.52
5
0.33
Find the mean value of X for any scoring play.
Calculate the variance of X.
Calculate the expected value of the random variable 𝑌 = 4𝑥 + 3.
Calculate the variance of the random variable 𝑌 = 4𝑥 + 3.
2. A four sided dice has an equal chance at landing on either 1,2,3 or
4. The probability distribution is given in the table below.
1
¼
𝑥
𝑃(𝑋 = 𝑥)
a.
b.
c.
d.
Calculate
Calculate
Calculate
Calculate
the
the
the
the
2
¼
3
¼
4
¼
mean of X.
variance of X.
expected value of the random variable 𝑌 = 30𝑥 + 10.
variance of the random variable 𝑌 = 30𝑥 + 10.
3. An investigation is carried out to determine the wages of a taxi
driver over the course of a week. It is found that the driver receives
a mean of $23.20 per hour in wet weather with a standard deviation
of $√4 and receives a mean of $16.40 per hour in fine weather with
a standard deviation of $√3.
a. Calculate the mean difference of the taxi driver’s wages.
b. Calculate the variance of the difference in the taxi driver’s wages.
4. A recipe for a cake mixture has two cups of flour and one cup of
sugar. The weight of flour in a cup is a random variable with mean
140 g and variance 5g. Similarly, the weight of sugar in a cup has a
mean 240g and variance 8g.
a. Calculate the mean of the two cups of flour and one cup of sugar.
b. Calculate the variance of the two cups of flour and one cup of sugar.