An ordinary (fair) coin is tossed 3 times. Outcomes are thus triples of "heads" (h) and "tails" () which we write hth, ttt, etc. For each outcome, let N be the random variable counting the number of tails in each outcome. For example, if the outcome is htt, then N (htt) = 2. Suppose that the random variable X is defined in terms of N as follows: X=2N²-4N-4. The values of X are given in the table below. Outcome Value of X Value X of X P(X=x) ttt hht hth tth tht 6-6 -4 -4 htt thh hhh -4 2 Calculate the probabilities P(X=x) of the probability distribution of X. First, fill in the first row with the values of X. Then fill in the appropriate probabilities in the second row. 0 -4-6 X S
An ordinary (fair) coin is tossed 3 times. Outcomes are thus triples of "heads" (h) and "tails" () which we write hth, ttt, etc. For each outcome, let N be the random variable counting the number of tails in each outcome. For example, if the outcome is htt, then N (htt) = 2. Suppose that the random variable X is defined in terms of N as follows: X=2N²-4N-4. The values of X are given in the table below. Outcome Value of X Value X of X P(X=x) ttt hht hth tth tht 6-6 -4 -4 htt thh hhh -4 2 Calculate the probabilities P(X=x) of the probability distribution of X. First, fill in the first row with the values of X. Then fill in the appropriate probabilities in the second row. 0 -4-6 X S
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 6E
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Transcribed Image Text:An ordinary (fair) coin is tossed 3 times. Outcomes are thus triples of "heads" (h) and "tails" () which we write hth, ttt, etc.
For each outcome, let N be the random variable counting the number of tails in each outcome. For example, if the outcome is htt, then N (htt) = 2. Suppose
that the random variable X is defined in terms of N as follows: X=2N²-4N-4. The values of X are given in the table below.
Outcome hht hth tth tht ttt
Value of X
-6 -6
-4
-4
2
Value .x of X
Calculate the probabilities P(X=x) of the probability distribution of X. First, fill in the first row with the values of X. Then fill in the appropriate probabilities
in the second row.
P(X=x)
0
htt thh hhh
-4
0
-4-6
00
X
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