Analysis and Approaches SL — Questionbank

All Concepts - Statistics and Probability

All questions in Topic 4 Statistics and Probability

Question 8

NO CALCULATOR

Spicy

[Maximum mark: 10]

Consider an arithmetic sequence with

$u_{1} = 0.5\ \ and\ u_{4} = 0.2$

(a) Find the common difference, d.

The following table shows the probability distribution of a discrete random variable X, where

P(X = n) = u_nk, n ∈ Z⁺, 1 ≤ n ≤ 4, k ∈ R⁺

n	1	2	3	4
P(X = n)	0.5k	u₂k	u₃k	0.2k

[2]

(b) Find the value of k

[3]

(c) Hence, write down the probability distribution of X.

[2]

(d) Find the expected value E(X)

[3]