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Quantitative Methods for Business & Management
Frank Dewhurst, UMIST, UK
Probability and Statistical Models
Self-test Questions
1
In throwing a pair of fair dice you calculate that the probability of throwing two sixes is 1/36. What sort of probability estimate is this?
A)
A priori
B)
Empirical
C)
Subjective direct
D)
Subjective indirect
E)
Guesswork
2
If estimating probability empirically, it does not matter how many observations are taken.
A)
TRUE
B)
FALSE
3
Which of the following statements is untrue?
A)
0 ≤ P(E) ≤ 1
B)
If E is certain then P(E) = 1
C)
P(E) = 1 / P(Ē)
D)
If P is impossible then P(E) = 0
E)
(4.0K)
4
If two outcomes cannot happen in the same experiment, they are called:
A)
Independent
B)
Mutually exclusive
C)
Empirical
D)
Mutually exhaustive
E)
Improbable
5
Which is the correct formula for the variance of a discrete probability distribution?
A)
(1.0K)
B)
(1.0K)
C)
(1.0K)
D)
(1.0K)
E)
(1.0K)
6
What is signified by the formula
(1.0K)
A)
Standard deviation of a probability distribution.
B)
Standard deviation of random variable.
C)
Variance of a random variable.
D)
Mean of a probability distribution.
E)
Mean of a random variable.
7
If X is a discrete random variable with has a uniform distribution defined as P(X=1)=P(x=2)=P(X=3)=P(X=4)=P(X=5)=0.2, then what is P(X ≤ 3)?
A)
0.2
B)
0.6
C)
1
D)
0
E)
0.4
8
The Binomial distribution defines the probability of obtaining x ________ in n trials.
A)
values
B)
random variables
C)
probabilities
D)
experiments
E)
successes
9
If P = 0.3 then the Binomial distribution is symmetrical.
A)
TRUE
B)
FALSE
10
Which single expression defines the mean and variance of a Poisson distribution?
A)
λ = n*P
B)
√λ = √(n*P)
C)
λ2 = (n*P)2
D)
(1 - λ) = (1 - nP)
E)
1 / λ = 1 / (n*P)
11
The Poisson distribution models the ________ of a number of (low probability) successes in n trials.
A)
random variable
B)
index
C)
quartile
D)
probability
E)
histogram
12
The Exponential and Normal distribution are ________ probability distributions
A)
outrageous
B)
variable
C)
continuous
D)
biased
E)
discrete
13
The mean and standard deviation of the exponential distribution are the same.
A)
TRUE
B)
FALSE
14
What are the mean and standard deviation of a standard normal distribution?
A)
μ=0 and σ=1
B)
μ=0 and σ=1/ μ
C)
μ=1 and σ=0
D)
μ=10 and σ=100
E)
μ=1 and σ=1
15
If X is a continuous random variable with mean μ, then P(X ≥ μ) = 0.5
A)
TRUE
B)
FALSE
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