Question

In the game Plinko on the television game show The Price is Right, contestants have the opportunity to earn “chips” (flat, circular disks) that can be dropped down a peg board into slots labeled with cash amounts. Every contestant is given one chip automatically and can earn up to four more chips by correctly guessing the prices of certain small items. If we let p denote the probability a contestant correctly guesses the price of a prize, then the number of chips a contestant earns, X, can be modeled as X = 1 + N, where N ~ Bin(4, p).

1. (a)Determine E(X) and Var(X).

2. (b)For each chip, the amount of money won on the Plinko board has the following distribution:

3. Value	$0	$100	$500	$1000	$10,000
   Probability	.39	.03	.11	.24	.23

   Determine the mean and variance of the winnings from a single chip.

4. (c) Let Y denote the total winnings of a randomly selected contestant. Using results from the previous section, the conditional mean and variance of Y, given a player gets x chips, are μx and σ ²x, respectively, where μ and σ ² are the mean and variance for a single chip computed in (b). Find expressions for the (unconditional) mean and standard deviation of Y. [Note: Your answers will be functions of p.]
5. (d) Evaluate your answers to part (c) for p = 0, .5, and 1. Do these answers make sense? Explain.

I need help with parts C and D here is a table with the values I got for part B

X	P(X)	XP(X)	(X-E(X))	(X-E(X))^2	(X-E(X))^2P(X)
0	0.39	0	-2598	6749604	2632345.56
100	0.03	3	-2498	6240004	187200.12
500	0.11	55	-2098	4401604	484176.44
1000	0.24	240	-1598	2553604	612864.96
10000	0.23	2300	7402	54789604	12601608.92
	E(X)	2598		Var(X)	16518196

Answer 1

EXCEL:

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