a. Suppose you are a contestant in JEETO PAKISTAN game show; there are four identical looking boxes containing 1000 Rs, 3000 Rs, 5000 Rs and 10000 Rs. You start the game by randomly choosing a box. Among the three unchosen boxes, the game show host opens the box that hold the median amount of money. (For example if the unopened boxes contains 1000 Rs, 5000 Rs and 10000 Rs, the host opens the 5000 Rs box). The host then ask you if you want to keep your box or switch one of the other remaining boxes. You refuse the host offer and open the box you first choose. Let Z is the reward in Rupees that you keep. Find the PMF of Z, E [Z] and VAR [Z].
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.
![a. Suppose you are a contestant in JEETO PAKISTAN game show; there are four identical
looking boxes containing 1000 Rs, 3000 Rs, 5000 Rs and 10000 Rs. You start the game by
randomly choosing a box. Among the three unchosen boxes, the game show host opens the
box that hold the median amount of money. (For example if the unopened boxes contains
1000 Rs, 5000 Rs and 10000 Rs, the host opens the 5000 Rs box). The host then ask you
if you want to keep your box or switch one of the other remaining boxes. You refuse the
host offer and open the box you first choose. Let Z is the reward in Rupees that you keep.
Find the PMF of Z, E [Z] and VAR [Z].](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9214e92a-2135-40f9-acb9-04fd0c612e58%2F53dc28ee-53f6-47f3-bfec-50daafc9f952%2Ffg87y2_processed.jpeg&w=3840&q=75)
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