Question Solved1 Answer Given the probability distributions shown to the right, complete the following parts. a. Compute the expected value for each distribution. b. Compute the standard deviation for each distribution. c. What is the probability that x will be at least 3 in Distribution A and Distribution B? d. Compare the results of distributions A and B. What is the standard Given the probability distributions shown to the right, complete the following parts. a. Compute the expected value for each distribution. b. Compute the standard deviation for each distribution. c. What is the probability that x will be at least 3 in Distribution A and Distribution B? d. Compare the results of distributions A and B. What is the standard deviation for distribution B? 6= (Type an integer or decimal rounded to three decimal places as needed.) c. What is the probability that x will be at least 3 in Distribution A? P(x ≥ 3) = (Type an integer or a decimal. Do not round.) What is the probability that x will be at least 3 in Distribution B? P(x ≥ 3) = A112OX Xi 0 4 Distribution A P(X=X₁) 0.50 0.22 0.15 0.10 0.03 Xi 0123 T 4 Distribution B P(X= x₁) 0.03 0.10 0.15 0.22 0.50 n

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Transcribed Image Text: Given the probability distributions shown to the right, complete the following parts. a. Compute the expected value for each distribution. b. Compute the standard deviation for each distribution. c. What is the probability that x will be at least 3 in Distribution A and Distribution B? d. Compare the results of distributions A and B. What is the standard deviation for distribution B? 6= (Type an integer or decimal rounded to three decimal places as needed.) c. What is the probability that x will be at least 3 in Distribution A? P(x ≥ 3) = (Type an integer or a decimal. Do not round.) What is the probability that x will be at least 3 in Distribution B? P(x ≥ 3) = A112OX Xi 0 4 Distribution A P(X=X₁) 0.50 0.22 0.15 0.10 0.03 Xi 0123 T 4 Distribution B P(X= x₁) 0.03 0.10 0.15 0.22 0.50 n
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Transcribed Image Text: Given the probability distributions shown to the right, complete the following parts. a. Compute the expected value for each distribution. b. Compute the standard deviation for each distribution. c. What is the probability that x will be at least 3 in Distribution A and Distribution B? d. Compare the results of distributions A and B. What is the standard deviation for distribution B? 6= (Type an integer or decimal rounded to three decimal places as needed.) c. What is the probability that x will be at least 3 in Distribution A? P(x ≥ 3) = (Type an integer or a decimal. Do not round.) What is the probability that x will be at least 3 in Distribution B? P(x ≥ 3) = A112OX Xi 0 4 Distribution A P(X=X₁) 0.50 0.22 0.15 0.10 0.03 Xi 0123 T 4 Distribution B P(X= x₁) 0.03 0.10 0.15 0.22 0.50 n
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Answer:- Given that: The following probability distributions are given, Distribution A : t tt tttxi tttP(X=xi) tt tt ttt0 ttt0.50 tt tt ttt1 ttt0.22 tt tt ttt2 ttt0.15 tt tt ttt3 ttt0.10 tt tt ttt4 ttt0.03 tt t Distribution B : t tt tttxi tttP(X=xi) tt tt ttt0 ttt0.03 tt tt ttt1 ttt0.10 tt tt ttt2 ttt0.15 tt tt ttt3 ttt0.22 tt tt ttt4 ttt0.50 tt t   (A) The expected value for each distribution is, Expected value for Distribution A : E(X)_(A)=sumx_(i)**P(X=x_(i))                  =0**0.50+1**0.22+2**0.15+3**0.10+4**0.03                  =0+0.22+0.3+0.3+0.12                  =0.94 Hence, the expected value for Distribution A = mu = 0.94   Expected value for Distribution B : E(X)_(B)=sumx_(i)**P(X=x_(i))                  =0**0.03+1**0.10+2**0.15+3**0.22+4**0.50                  =0+0.10+0.3+0.66+2                  =3.06 Hence, the expected value for Distribution B = mu = 3.06     (B) The standard deviation for each distribution is,   Standard deviation for Distribution A: SD_(A)=sqrt(E(X^(2))_(A)-[E(X)_(A)]^(2))   E(X^(2))_(A)=sumx_(i)^(2)**P(X=x_(i))                  =0^(2)**0.50+1^(2)**0.22+2^(2)**0.15+3^(2)**0.10+4^(2)**0.03 =0+0.22+0.6+0.9+0.48 =2.2                   SD_(A)=sqrt(E(X^(2))_(A)-[E(X)_(A)]^(2))                      =sqrt(2.2-[0.94]^(2))              =sqrt(2.2-0.8836)             &#16 ... See the full answer