5.1 basics of probability distributions. compute the mean and standard deviation of a discrete random…
5.1 basics of probability distributions. compute the mean and standard deviation of a discrete random variable.\nthe ohio lottery has a game called pick 4 where a player pays $1 and picks a four - digit number. if the four numbers come up in the order you picked, then you win $3100.\na) write the probability distribution for a players winnings.\nfill in the table below.\nfor the computer to grade this one correctly make sure that your x values are from smallest to largest.\n|x|p(x)|\n|\n|\n|\n|\nb) what are your expected winnings?\nround final answer to 2 decimal places. put correct units in the second box.\n|\n|\nc) which of the following is the correct interpretation of the expected winnings?\nselect an answer\nquestion help: video message instructor post to forum\nsubmit question
Answer
Explanation:
Step1: Determine possible outcomes
The player pays $1. If they lose, their net - winning $X=- 1$. The probability of losing $P(X = - 1)$ is $\frac{9999}{10000}$ since there are $10000$ possible four - digit numbers from $0000$ to $9999$ and only $1$ winning number. If they win, their net - winning $X = 3100 - 1=3099$ (subtracting the $1$ they paid to play), and the probability of winning $P(X = 3099)$ is $\frac{1}{10000}$.
Step2: Calculate expected value formula
The formula for the expected value $E(X)=\sum_{i}x_{i}P(x_{i})$. Here, $E(X)=(-1)\times\frac{9999}{10000}+3099\times\frac{1}{10000}$.
Step3: Compute expected value
[ \begin{align*} E(X)&=\frac{-9999 + 3099}{10000}\ &=\frac{-6900}{10000}\ &=- 0.69 \end{align*} ]
Answer:
a)
| $X$ | $P(X)$ |
|---|---|
| -1 | $\frac{9999}{10000}$ |
| 3099 | $\frac{1}{10000}$ |
| b) -0.69 dollars | |
| c) On average, a player can expect to lose $0.69$ per game. |