Comprehensive Review of Discrete Probability Distributions and Expected Values

this video is a review for this Creator distribution in discrete distribution the data is a

discrete the summation of the probability equals what

all the probabilities will be God from the table expected a value e of x equals summation

of x times the probability of a random or variable equals X when the expected value equals zero

means the gamma is fair for example let be the number of breakdowns of machine B on any given day the

probability distribution for B can be modeled by the following table find Acts

according to summation of probability equals what

we can set up 0.7 plus 0.2 Plus 0.08 plus x equals 1.

then x equals 0.02 for p find the expected value e of B

equals zero times 0.7 plus 1 times 0.2

plus 2 times 0.08 plus 3 times 0.02 equals 0.42

let's go to say probability of 4 B greater than what

that equals probability of a b equals 2 plus probability of a b

equals three so we have what 0.08 plus 0.02

equals 0.1 for d find the probability of B less than or

equal to 1. which means the probability of B equals zero plus probability of a b

equals what equals 0.7 plus 0.2

equals 0.9 let's go to question three a game is played where two unbox the

dice are rolled another score in the game is the greater of the two numbers shown if the two numbers are the same

then the score in the game is the number shown on one of the dice a diagram showing the possible outcomes

is given below let T be the random variable the score in a game complete the table to show the

probability distribution of t the score in the game is the greater of the two numbers shown

first the dice second dice we will write down all the

score in this diagram one two

three 4 4 5 6.

because in this diagonal we have the same score on both dice

two three four five six

this is a two three four five six four five six

this is a three three four four four five six

five five five five six this is the all six

now all together is a 36. we have only one one over thirty six

we have all one two three twos let's go to three

one two three four five over thirty six in this way you can figure out all the

probability for each number make sure the summation of the probability equals one you can check

let's go to B find the probability that a player scores at least three in a game we're looking for the probability

remember we use the T as the random variable in this problem so we write down probability of t

greater than equal to 3. we need to add up all these four

probability together 5 over 36 plus 7 over 36 plus 9 over 36.

plus 11 over 36 equals 32 over 36 8 over 9. let's go to say

find the probability that a player scores six given that this card at least three

promo formula booklet we find the conditional probability

formula probability of a given B equals the probability of a intersection

B over probability of a b given that they score at least three so we are looking for probability of for

t equals 6. given that t greater than or equal to 3.

equals we do know probability of T equals six intersection T greater than or equal to 3 equals probability

T equals a six so we get probability of T equals six over probability of

T greater than equal to 3. count this is a this is a b then you can use this formula to figure

out the answer probability of T equals 6 is here 11 over 36

probability of T greater than or equal to three we will use this one

because we can reduce the denominator easily final answer is 11 over 32. let's go to the find the expected score

of the game use the formula expected

value equals 1 times 1 over 36.

plus 2 times 3 over 36 plus 3 times the 5 over 36 Plus

4 times the seven over thirty six plus a 5 times 9 over 36 plus 6 times 11 over 36.

161 over 36 [Music]