A particular coin is biased. Each time it is flipped, the probability of a head is P (H) = 0.95 and the probability of a tail is P(T) = 0.05. Each flip is independent of the other flips. The coin is flipped twice. Let X be the total number of times the coin shows a head out of two flips. So the possible values of X are x = 0, 1, or 2. a) How would we find P(X= 2) ? (Pick all right answers) Type in Rstudio: choose(1, 1)* 0.95^0 * 0.05^2 Type in Rstudio: choose(2, 2)* 0.95^2 * 0.05^0 □ P(X = 2) = (²) P(H)² (1 – P(H))²—2 □ P(X = 2) = (₁) P(H)¹ (1 – P(H))2–1 Knowing that P(X = 1) = 0.095 and P(X= 2) = 0.9025 P(X = 0) = 0.0025 (Enter the exact value) b) What is the probability that X≥ 1? 0.0025 (Enter the exact value) c) Compute the expected value of X. μχ = d) Compute the variance X. of = (Enter the exact value) (Enter the exact value) compute the following probabilities:
A particular coin is biased. Each time it is flipped, the probability of a head is P (H) = 0.95 and the probability of a tail is P(T) = 0.05. Each flip is independent of the other flips. The coin is flipped twice. Let X be the total number of times the coin shows a head out of two flips. So the possible values of X are x = 0, 1, or 2. a) How would we find P(X= 2) ? (Pick all right answers) Type in Rstudio: choose(1, 1)* 0.95^0 * 0.05^2 Type in Rstudio: choose(2, 2)* 0.95^2 * 0.05^0 □ P(X = 2) = (²) P(H)² (1 – P(H))²—2 □ P(X = 2) = (₁) P(H)¹ (1 – P(H))2–1 Knowing that P(X = 1) = 0.095 and P(X= 2) = 0.9025 P(X = 0) = 0.0025 (Enter the exact value) b) What is the probability that X≥ 1? 0.0025 (Enter the exact value) c) Compute the expected value of X. μχ = d) Compute the variance X. of = (Enter the exact value) (Enter the exact value) compute the following probabilities:
Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter14: Counting And Probability
Section14.2: Probability
Problem 3E: The conditional probability of E given that F occurs is P(EF)=___________. So in rolling a die the...
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Can you use the Rstudio to calculate some value please. Thank you!
Transcribed Image Text:A particular coin is biased. Each time it is flipped, the probability of a head is P (H) = 0.95 and the probability of a
tail is P(T) = 0.05. Each flip is independent of the other flips. The coin is flipped twice. Let X be the total number of
times the coin shows a head out of two flips. So the possible values of X are x = = 0, 1, or 2.
a) How would we find P(X=2) ? (Pick all right answers)
Type in Rstudio: choose(1, 1)* 0.95^0 * 0.05^2
✔ Type in Rstudio: choose(2, 2)* 0.95^2 * 0.05^0
□ P(X = 2) = (²) P(H)² (1 – P(H))²—2
○ P(X = 2) = (²)P(H)¹ (1 — P(H))²–1
Knowing that P(X = 1) = 0.095 and P(X= 2) = 0.9025 , compute the following probabilities:
P(X=0)
= 0.0025
(Enter the exact value)
b) What is the probability that X ≥ 1?
0.0025
(Enter the exact value)
c) Compute the expected value of X.
"X=
d) Compute the variance X.
0²=
=
(Enter the exact value)
(Enter the exact value)
Transcribed Image Text:b) What is the probability that X ≥ 1?
0.0025
(Enter the exact value)
c) Compute the expected value of X.
μ.Χ
d) Compute the variance X.
of
=
(Enter the exact value)
e) What is the name of the distribution that can be used to model X?
Binomial
g) Let Y be the random variable Y =
μy =
(Enter the exact value)
f) What are the values of parameters for the distribution selected in part e)?
Parameters are n = Number
and p = Number
X
50
. (Enter the exact values)
Compute the expected value of Y.
(Enter the exact value)
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