Consider the following game: Four cards marked 0, 1, 2 and 3 are shu ed and one card is picked randomly. The number on that card is noted, it is replaced in the small deck, but all cards with a higher number are removed. Then, the remaining cards are shu ed again and one card is picked randomly. Calculate the expectation and standard deviation for the sum of the numbers on the two picked cards.
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
Consider the following game: Four cards marked 0, 1, 2 and 3 are shu ed and one card is picked randomly. The number on that card is noted, it is replaced in the small deck, but all cards with a higher number are removed. Then, the remaining cards are shu ed again and one card is picked randomly. Calculate the expectation and standard deviation for the sum of the numbers on the two picked cards.
The different combinations of two cards are:
The probability mass function of the experiment is given below.
| X | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
| P(X) | 1/10 | 1/10 | 1/10 | 2/10 | 2/10 | 1/10 | 1/10 |
Use the equation to find the expected value of X.
Therefore, the expected value is 2.8.
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