Question 2 Let X be a discrete random variable with probability mass function given by 1 2 3 p(x) 1/4 1/2 1/8 1/8 a) Estimate P(X < 1). Answer: в «- 1000 x <- replicate(B, sample( c(0, 1, 2, 3), 1, prob = c(1/4, 1/2, 1/8, 1/8) ) mean (x <= 1) ## [1] 0.76 # answer (1/4) + (1/2) ## [1] 0.75 b) Find P(X <1|X < 2). Answer: B <- 1000 x <- replicate (B, sample( c(0, 1, 2, 3), 1, prob = c(1/4, 1/2, 1/8, 1/8) ), y <- replicate(B, sample( c(0, 1, 2, 3), 1, prob = c(1/4, 1/2, 1/8, 1/8) ) mean (x <= 1)/mean (y <= 2)
Question 2 Let X be a discrete random variable with probability mass function given by 1 2 3 p(x) 1/4 1/2 1/8 1/8 a) Estimate P(X < 1). Answer: в «- 1000 x <- replicate(B, sample( c(0, 1, 2, 3), 1, prob = c(1/4, 1/2, 1/8, 1/8) ) mean (x <= 1) ## [1] 0.76 # answer (1/4) + (1/2) ## [1] 0.75 b) Find P(X <1|X < 2). Answer: B <- 1000 x <- replicate (B, sample( c(0, 1, 2, 3), 1, prob = c(1/4, 1/2, 1/8, 1/8) ), y <- replicate(B, sample( c(0, 1, 2, 3), 1, prob = c(1/4, 1/2, 1/8, 1/8) ) mean (x <= 1)/mean (y <= 2)
College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter9: Counting And Probability
Section9.3: Binomial Probability
Problem 2E: If a binomial experiment has probability p success, then the probability of failure is...
Related questions
Question
100%
This is a Statistics problem. Please code in R if needed.
The problem I'm having difficulty understanding is shown below:
![Question 2
Let X be a discrete random variable with probability mass function given by
1
2
3
p(x) 1/4 1/2 1/8 1/8
a) Estimate P(X < 1).
Answer:
B <- 1000
x <- replicate (B,
sample( c(0, 1, 2, 3), 1, prob
c(1/4, 1/2, 1/8, 1/8) )
mean (x <= 1)
## [1] 0.76
# answer
(1/4) + (1/2)
## [1] 0.75
b) Find P(X <1 | X < 2).
Answer:
B <- 1000
x <- replicate (B,
sample( c(0, 1, 2, 3), 1, prob = c(1/4, 1/2, 1/8, 1/8) ),
y <- replicate(B,
sample( c(0, 1, 2, 3), 1, prob
с (1/4, 1/2, 1/8, 1/8) )
mean (x <= 1)/mean (y <= 2)
## [1] 0.8963134
# answer
(1/4 + 1/2) / (1/4 + 1/2 + 1/8)
## [1] 0.8571429](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcb9da028-c1e8-4fb4-9df2-7f4287e8030e%2F6aa38585-6abe-4e5a-9f58-99702569fb0e%2Fsw45pp8_processed.png&w=3840&q=75)
Transcribed Image Text:Question 2
Let X be a discrete random variable with probability mass function given by
1
2
3
p(x) 1/4 1/2 1/8 1/8
a) Estimate P(X < 1).
Answer:
B <- 1000
x <- replicate (B,
sample( c(0, 1, 2, 3), 1, prob
c(1/4, 1/2, 1/8, 1/8) )
mean (x <= 1)
## [1] 0.76
# answer
(1/4) + (1/2)
## [1] 0.75
b) Find P(X <1 | X < 2).
Answer:
B <- 1000
x <- replicate (B,
sample( c(0, 1, 2, 3), 1, prob = c(1/4, 1/2, 1/8, 1/8) ),
y <- replicate(B,
sample( c(0, 1, 2, 3), 1, prob
с (1/4, 1/2, 1/8, 1/8) )
mean (x <= 1)/mean (y <= 2)
## [1] 0.8963134
# answer
(1/4 + 1/2) / (1/4 + 1/2 + 1/8)
## [1] 0.8571429
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps
Recommended textbooks for you
College Algebra
Algebra
ISBN:
9781305115545
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Holt Mcdougal Larson Pre-algebra: Student Edition…
Algebra
ISBN:
9780547587776
Author:
HOLT MCDOUGAL
Publisher:
HOLT MCDOUGAL
College Algebra
Algebra
ISBN:
9781305115545
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Holt Mcdougal Larson Pre-algebra: Student Edition…
Algebra
ISBN:
9780547587776
Author:
HOLT MCDOUGAL
Publisher:
HOLT MCDOUGAL