IEE 380 EXAM 1 QUESTIONS & ANSWERS
The probability a lab specimen contains high levels of contamination is 0.15. A group of
3 independent samples are checked.
What is the probability that exactly one sample contains high levels of contamination?
0.3251
P(H1 n H2' n H3') + P(H1' n H2 n H3') + P(H1' n H2' n H3)
In Siberia there is a probability of 0.50 that a person is wearing a fur coat, in Urals there
is a probability of 0.70 that a person will be wearing a fur coat. There is a probability of
.60 that you are in Siberia and a probability of 0.40 that you are in Urals.
What is the probability that a person is not wearing a fur coat?
N = Not wearing a fur coat
S = In Siberia
U = In Urals
P(N) = P(N|S) x P(S) + P(N|U) x P(U) = 0.42
What is another term for mean?
Expected value
For the case of the thin copper wire, suppose that the number of flaws, X, follows a
Poisson distribution with a rate of 2.3 flaws per mm. A 2mm piece of wire is defective if
it contains at least 1 flaw. What is the probability there are no defective pieces of wire if
we sample fifty 2mm pieces?
Lambda = 2.3
T=2
P(X=0) = possionpdf(2.3(2), 0) = 0.1005
P(Y=50) = binompdf(50, 0.1005, 50) = 0
Therefore the probability is 0
, Let the continuous random variable X denote the current measured in a thin copper wire
in milliamperes (mA). Assume that the range of X is 4.9 <= x <= 5.1 and f(x) = 5.
What is the probability that a current is less than 5mA?
Continuous so P(X < 5) = integral from 4.9 to 5.0 of 5dx = 0.50
The time until a chemical reaction is complete in ms is approximated by this cumulative
distribution function:
F(x) = 0 for x < 0 and 1-e^(-0.01x) for 0 <= x
What proportion of reactions is complete within 200ms?
P(X < 200) = P (X <= 200) = F(200) = 1-e^(-0.01(200)) = 0.8647
The random variable X has a continuous uniform distribution on [4.9, 5.1].
The pdf of X is f(x) = 5, 4.9 <= x <= 5.
What is the probability that a measurement is between 4.95 and 5.00?
P(4.95 < x < 5.00) = integral from 4.95 to 5.00 of 5dx = 0.25
Suppose the measurements in a strip of wire are assumed to follow a normal
distribution with a mean of 10 and a standard deviation of 2. Determine the value for
which the probability a current measurement is below 0.98.
P(X < x) = 0.98
invNorm(0.98, 10, 2, Left) = 14.107
The combination rule determines the number of ways a selection of x items from a set
of n available items can happen if we assume order does not matter.
True
Which of the following is not true?
1. A discrete sample space can be made up of a finite set of outcomes.
2. All of these options are not true.
3. If S is the sample space, then the P(S) = 0.
4. A continuous random variable is one with an interval of real numbers for its range.
5. Probabilities are numbers in the [0,1] interval.
If S is the sample space, then the P(S) = 0.
The probability a lab specimen contains high levels of contamination is 0.15. A group of
3 independent samples are checked.
What is the probability that exactly one sample contains high levels of contamination?
0.3251
P(H1 n H2' n H3') + P(H1' n H2 n H3') + P(H1' n H2' n H3)
In Siberia there is a probability of 0.50 that a person is wearing a fur coat, in Urals there
is a probability of 0.70 that a person will be wearing a fur coat. There is a probability of
.60 that you are in Siberia and a probability of 0.40 that you are in Urals.
What is the probability that a person is not wearing a fur coat?
N = Not wearing a fur coat
S = In Siberia
U = In Urals
P(N) = P(N|S) x P(S) + P(N|U) x P(U) = 0.42
What is another term for mean?
Expected value
For the case of the thin copper wire, suppose that the number of flaws, X, follows a
Poisson distribution with a rate of 2.3 flaws per mm. A 2mm piece of wire is defective if
it contains at least 1 flaw. What is the probability there are no defective pieces of wire if
we sample fifty 2mm pieces?
Lambda = 2.3
T=2
P(X=0) = possionpdf(2.3(2), 0) = 0.1005
P(Y=50) = binompdf(50, 0.1005, 50) = 0
Therefore the probability is 0
, Let the continuous random variable X denote the current measured in a thin copper wire
in milliamperes (mA). Assume that the range of X is 4.9 <= x <= 5.1 and f(x) = 5.
What is the probability that a current is less than 5mA?
Continuous so P(X < 5) = integral from 4.9 to 5.0 of 5dx = 0.50
The time until a chemical reaction is complete in ms is approximated by this cumulative
distribution function:
F(x) = 0 for x < 0 and 1-e^(-0.01x) for 0 <= x
What proportion of reactions is complete within 200ms?
P(X < 200) = P (X <= 200) = F(200) = 1-e^(-0.01(200)) = 0.8647
The random variable X has a continuous uniform distribution on [4.9, 5.1].
The pdf of X is f(x) = 5, 4.9 <= x <= 5.
What is the probability that a measurement is between 4.95 and 5.00?
P(4.95 < x < 5.00) = integral from 4.95 to 5.00 of 5dx = 0.25
Suppose the measurements in a strip of wire are assumed to follow a normal
distribution with a mean of 10 and a standard deviation of 2. Determine the value for
which the probability a current measurement is below 0.98.
P(X < x) = 0.98
invNorm(0.98, 10, 2, Left) = 14.107
The combination rule determines the number of ways a selection of x items from a set
of n available items can happen if we assume order does not matter.
True
Which of the following is not true?
1. A discrete sample space can be made up of a finite set of outcomes.
2. All of these options are not true.
3. If S is the sample space, then the P(S) = 0.
4. A continuous random variable is one with an interval of real numbers for its range.
5. Probabilities are numbers in the [0,1] interval.
If S is the sample space, then the P(S) = 0.
