Probability Mass Function
Let X be the random variable representing the number of heads obtained in two tosses. List the outcome for X=0 (no heads)
{T, T}
Given A and B are disjoint events, what is the expression for P(AUB)?
P(A) + P(B)
What’s the range for any event's probability?
Between 0 and 1, inclusive
A coin is tossed and a die is rolled at the same time. How many outcomes are in the sample space, S?
12
x 0 1 2 3
p(x) 0.2 0.1 0.3 ?
0.4
If 1 in 100 people is randomly drawn where 40 are allergic to pollen, 10 people own a car and are allergic to pollen, and 30 people own a car and aren’t allergic to pollen, what’s the probability the person drawn owns a car?
40/100 = 2/5 = 0.4
List 2 of the conditions that need to be true for a distribution to be Binomial.
1. The number of trials is fixed
2. The probability of success is the same for each trial
3. The random variable counts the number of successes
4. The trials are independent
How many ways can the word ‘table’ be arranged?
120 = 5!
The pdf of a continuous RV X is given by:
f(x) = { 3(1 − x)^2 if 0 < x < 1
0 otherwise
Compute P(X < 0.5)
0.875 = 7/8
If 1 in 100 people is randomly drawn where 40 are allergic to pollen, 10 people own a car and are allergic to pollen, and 30 people own a car and aren’t allergic to pollen, what’s the probability the person drawn does not own a car and is not allergic to pollen?
30/100 = 3/10 = 0.3
A die has probability of 1/6 to roll a 2. Let X=1 if a 2 is rolled, and X=0 otherwise. What is the distribution of X if the die is rolled 4 times?
X ~ Bin(4, 1/6)
A 7-place license plate consists of 5 letters followed by 2 numbers. How many such license plates are possible?
265 * 102 = 1,188,137,600