A sample space has four possible discrete outcomes: S={1,2,3,4} with probabilities 0.1, 0.2, 0.3, 0.4 respectively....

A sample space has four possible discrete outcomes: S={1,2,3,4} with probabilities 0.1, 0.2, 0.3, 0.4 respectively.
a) Sketch the density function fx(x)
b) Write the equation for the density function
c) Calculate the probability of outcomes between 2 and 3 inclusively
d) Sketch the distribution function Fx(x)
e) Write the equation of the distribution function
f) Use the distribution function to calculate the probability of outcomes between 2 and 3 inclusively (don't forget to use the next lower outcome for the lower limit)

Solutions

Expert Solution

The sample space is with probabilities 0.1, 0.2, 0.3, 0.4 respectively.

a) The PMF is plotted below.

R code below:

X <- 1:4
P <- X/10
plot(1:1)
dev.new()
plot(X,P, xlim=c(0,5),ylim = c(0,0.5), lwd=2, type="h", col = "blue", xlab="X", ylab = "f(X)", main="PMF")

b) The PMF is

c) The probability,

d) The cumulative PMF (distribution function) is plotted below.

R code below:

X <- 1:4
P <- X/10

plot(1:1)
dev.new()
plot(X,cumsum(P), xlim=c(0,5),ylim = c(0,1.0), lwd=2, type="h", col = "blue", xlab="X", ylab = "F(X)", main="Cumulative PMF")
e) The distribution function is

f)The probability,

orchestra answered 1 year ago

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