Let S={s1,s2,s3} be a sample space with probability distribution P given by P(s1)-0.2, P(s2)=0.3, P(s3)=0.5. Let f be a function defined on S by f(s1)=5, f(s2)=-2, f(s3)=1. What is the expected value of f?
sum the products of P(si)*f(si) for i=1..3
To find the expected value of f, we need to multiply each value of f by its corresponding probability and sum them up.
The expected value of f, denoted as E(f), is given by:
E(f) = Σ (f(si) * P(si))
where si is an element of S.
Given the probability distribution P and the function values f for each element in S, we can calculate the expected value as follows:
E(f) = (f(s1) * P(s1)) + (f(s2) * P(s2)) + (f(s3) * P(s3))
Substituting the given values, we have:
E(f) = (5 * 0.2) + (-2 * 0.3) + (1 * 0.5)
Simplifying, we get:
E(f) = 1 + (-0.6) + 0.5
E(f) = 0.9
Therefore, the expected value of f is 0.9.
To find the expected value of a function, you need to multiply each outcome by its probability and sum them up.
In this case, we have the function f defined on the sample space S, and the corresponding probability distribution P for S.
The expected value of f (denoted as E[f]) can be calculated using the formula:
E[f] = ∑ (f(si) * P(si)) for all si in S
Let's calculate it step by step:
1. Multiply each outcome of f with its corresponding probability:
f(s1) * P(s1) = 5 * 0.2 = 1
f(s2) * P(s2) = -2 * 0.3 = -0.6
f(s3) * P(s3) = 1 * 0.5 = 0.5
2. Sum up the values obtained:
E[f] = 1 + (-0.6) + 0.5 = 0.9
Therefore, the expected value of f is 0.9.