Statistics and random variables

[anon15837621]

If I have an instrument system with 4 components and can function of at least two of them are working. Each component independently works with probability of 0.9.

How I can compute the probability that the system will function, using Rstudio functions?

[woodward]

It's a binomial probability distribution with p = 0.9. You need to add the values for x = 2:4.

# probabilities of 0-4 successes
dbinom(x = 0:4, size = 4, prob = 0.9)
#> [1] 0.0001 0.0036 0.0486 0.2916 0.6561

^{Created on 2020-11-16 by the reprex package (v0.3.0)}

[anon15837621]

@woodward

It's a binomial probability distribution with p = 0.9

but is pbinom or dbinom ?
p <- 0.8
n = 4
X <- 2:4
Prob <- pbinom(X, n, p)

[woodward]

They're basically the same, except pbinom gives the cumulative probabilities. You're less likely to make mistakes using dbinom.

# probabilities of x = 0-4 successes out of size = 4
size = 4
prob = 0.9
x <- 0:size
set.seed(123)

# probability density
d <- dbinom(x = x, size = size, prob = prob) 
plot(x, d, main = "Probability of x successes")

# cumulative probability density
p <- pbinom(q = x, size = size, prob = prob) 
plot(x, p, main = "Probability of x successes or less")

# inverse function
q <- qbinom(p = (0:100)/100, size = size, prob = prob) 
plot(q, (0:100)/100, main = "Inverse cumulative density function")

# generate random numbers
r <- rbinom(n = 10000, size = size, prob = prob) 
hist(r, main = "10000 Samples")

^{Created on 2020-11-17 by the reprex package (v0.3.0)}

[anon15837621]

Ok, but why is 0:4 and not 2:4 ? 2 of them are working.

[woodward]

Yeah you just need to add the ones for 2:4.