AP Statistics · Topic 4.8
Mean and Standard Deviation of Random Variables Practice
Part of Probability, Random Variables, and Probability Distributions.(VAR-5.B)
Practice questions
12
Sample questions
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Sample 1difficulty 2/5
The probability distribution of X is shown.
What is E(X)?
- Acheck_circle
1.1
- B
0.9
- C
1.0
- D
1.5
Why
E(X) = 0(0.2) + 1(0.5) + 2(0.3) = 0 + 0.5 + 0.6 = 1.1.
- A
Sample 2difficulty 3/5
Roll a fair die. E(X) =
- A
2.5
- B
3
- C
4
- Dcheck_circle
3.5
Why
(1+2+3+4+5+6)/6 = 21/6 = 3.5.
- A
Sample 3difficulty 3/5
Var(X) = E[(X − μ)²] for a discrete RV with possible values x_i is
- A
Σ x_i·P(x_i)
- Bcheck_circle
Σ (x_i − μ)²·P(x_i)
- C
Σ (x_i − μ)·P(x_i)
- D
(E(X))²
Why
Squared deviation weighted by probability.
- A
Sample 4difficulty 3/5
For a discrete RV X, E(X) =
- A
Σ x²
- Bcheck_circle
Σ x·P(X=x)
- C
1
- D
Σ P(X=x)
Why
E(X) is the probability-weighted sum.
- A
Sample 5difficulty 3/5
A random variable X has Var(X) = 0.49.
What is the standard deviation of X?
- A
0.49
- B
1.4
- C
0.24
- Dcheck_circle
0.7
Why
SD(X) = sqrt(Var(X)) = sqrt(0.49) = 0.7.
- A