The discrete random variable Y has probability distribution | y | 1 | 2 | 3 | 4 | |---|---|---|---|---| | P(Y = y) | a | b | 0.3 | c | where a, b and c are constants - Edexcel - A-Level Maths Statistics - Question 3 - 2011 - Paper 2

To find the values of a, b, c, and d, we start with the probability distribution. Since the sum of all probabilities must equal 1:

a + b + 0.3 + c = 1 \tag{1}

From the cumulative distribution function F(y), we have:

• For y = 1, F(1) = P(Y \leq 1) = 0.1, which implies ( a = 0.1 )
• For y = 2, F(2) = P(Y \leq 2) = 0.5, thus we have: F(2) = a + b = 0.5 \tag{2} Substituting (1) into (2), we get:

0.1 + b = 0.5 \Rightarrow b = 0.4 \tag{3}

Next, substituting values of a and b into (1):

0.1 + 0.4 + 0.3 + c = 1 \Rightarrow c = 0.2 \tag{4}

Finally, for d, since F(4) = 1, F(4) = 0.1 + 0.4 + 0.3 + d = 1 \Rightarrow d = 1 - 0.8 = 0.2 \tag{5}

In summary:

• a = 0.1
• b = 0.4
• c = 0.2
• d = 0.2