PLEASE SHOW STEPS 1 Give the sample space for an experiement

PLEASE SHOW STEPS!

1.

Give the sample space for an experiement in which a die is rolled and the outcomes are recorded.

2.

A) In a chess tournament consisting of 50 people, everyone plays everyone else. How many games are there total?

B) A box in a certain supply room contains four 60-W lightbulbs and five 75W lightbulbs. suppose three bulbs are randomly selected from the box. what is the probablility that exactly two of the selected bulbs are 75W?

3.

Let X be a continuous random variable with PDF fx(x) equal to:

Fx(x)={(k/6)x, 0<=x<=4 and 0 otherwise

A) find the value of the multiplicative constant k such that fx(x) is a legitimate PDF.

B) find the mean(expected value) of X.

C) Find the median of X.

Solution

1.

s = {1,2,3,4,5,6}

2.

a) We pair them witch each other, so there are 50C2 = 1225 games.

b)

There are 9C3 ways to choose any 3 lightbulbs.

Meanwhile, there are (5C2)(4C1) ways to choose 2 75W and 1 60W bulb.

Thus,

P = [(5C2)(4C1)]/(9C3) = 0.333333333 [answer]

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