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Descrete Distributions Sample Assignment

Questions: - During one holiday seasons, the Texas lottery played a game called the Stocking Stuffer. With this game, total instant winnings of $34.8 million were available in 70 million $1 tickets, with ticket prizes ranging from $1 to $1,000. Shown here are the various prizes and the probability of winning each prize. Use these data to compute the expected value of the game, the variance of the game, and the standard deviation of the game.

Prize (x)            Probability P(x)
$1,000___________.00002
100_____________.00063
20______________.00400
10______________.00601
4_______________.02403
2_______________.08877
1_______________.10479
0_______________.77175
_______________________________

Solutions: - The mean is computed as follows.

Prize(x)            Probability P(x)        x.P(x)
$1,000_______.00002 ________.02000
100_________.00063_________.06300
20__________.00400_________.08000
4___________.00601_________.06010
2___________.02403_________.09612
1___________.08877_________.17754
0___________.77175_________.00000
__________________∑[x.P(x)] = .60155
μ = E(x) = ∑[x.P(x)] = .60155
______________________________________________________

The expected payoff for a $1 ticket in this game is 60.2cents. If a person plays the game for a long time, he or she could expect to average about 60 cents in winnings. In the long run, the participant will lose about $1.00 – .602 = .398, about 40 cents a game. Of course, an individual will never win 60 cents in any one game.
Using this mean, μ = .60155, the variance and standard deviation can be computed as follows.

x       _____ P(x)           __ (x – μ)²            ____ (x – μ)² .P(x)
$1,000___.00002_____998797.26190_____19.97595
100_____.00063_____9880.05186_______-6.22443
20______.00400_____376.29986________-1.50520
10______.00601_____88.33086_________-0.53087
4_______.02403_____11.54946_________-0.27753
2_______.08877_____1.95566__________-0.17360
1_______.10479_____0.15876__________-0.01664
0_______.77175_____0.36186__________-0.27927
_____________________∑[(x – μ)² .P(x)] = 28.98349
        σ² = ∑[(x – μ)² .P(x)] = 28.98349
    σ = √ σ² = √∑[(x – μ)² .P(x)] = √28.98349 =    5.38363
The variance is 28.98349 (dollors)2 and the standard deviation is $5.38.

Other Sample Assignments in Statistics Homework Assignment :

Continious Distribution	Descrete Distributions
Descriptive Statistics	Nonparamatric Statistics
Probability	Sampling And Sampling Distribution
Statistical Inference Estimation For Single Popula	Simple Regression Analysis
Statistical Inference About 2 Population	Time Series Forcasting Index Number
Statistical Quality Control	Correlation
Index Number	Larger Sample Mean Proportions
Non Parametric Test	Probability Theory
Sampling Distribution	Simple and Multiple Linear Regression Analysis
Unvariate Analysis

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