Quiz questions

Find $c$ The random variable $R$ has pmf $p(r)=cr$ for $r=0,1,2,\mathrm{\dots },10$, where $c$ is a constant. Find the value of $c$.

(A) 0, (B) 1/10, (C) 1, (D) 1/55, (E) 10.

Dice Suppose two dice are rolled. Let $R$ be the maximum value to appear on the two rolls. What is the probability that $R$ is even?

(A) 1/3, (B) 5/12, (C) 1/2, (D) 7/12, (E) 2/3.

Variance The rv $R$ has pmf $p(r)=1/10$ for $r=1,2,\mathrm{\dots },10$. Find $\text{𝗏𝖺𝗋}(R)$.

(A) 0, (B) 8.25, (C) 10, (D) 38.5, (E) 68.06

Seeded Dice Throws Use the seed number 565 and simulate 200 rolls of a fair 6 sided dice. How many times did the number 5 occur?
(A) 31, (B) 32, (C) 33, (D) 34, (E) 35

Simulating the Lottery The UK National lottery (Lotto) involves the drawing of 6 numbered balls from a set of balls numbered 1 to 59. Which of the following commands will simulate a single realisation of a National lottery draw.

1. (A)

   sample(1:59, 6, replace=TRUE , prob=rep(1/59,59))

2. (B)

   sample(1:6, 59, replace=TRUE, prob=c(1/59,1/58,1/57,1/56,1/55,1/54))

3. (C)

   sample(1:59, 6, replace=FALSE, prob=rep(1/59,59))

4. (D)

   sample(1:6, 59, replace=FALSE, prob=c(1/59,1/58,1/57,1/56,1/55,1/54))

5. (E)

   sample(1:59, 6, replace=FALSE, prob=1/(59:1))