Suppose I work in a factory which does not have the best safety record. On any given day (independent of all other days) there is a 5% chance that there will be a workplace injury. Let X be the number of days until we have a workplace injury.

What is the distribution of X? Give the name of the distribution and the appropriate parameters.

What is the mean and variance of this distribution? Give your answer as a number,

but include the formulas (or logic) used.

What is the probability that there will be an injury within the next 5 workdays?

i. e. what is

P(X≤5)?

2

Let’s say a few employees have a rather inappropriate betting pool on which day

the next injury will occur. If I placed my wager on day 4, what is the probability

that I win?

1. The distribution of X, ,

Mean of the distribution, ,

Variance of X =

2. Probability that there would be an injury in the next 5 working days = 0.2263

3. Probability of winning = 0.0407

Step-by-step explanation:

1. Let us denote the number of days until there's a work place injury by

then Probability of having a work place injury

and Probability of having no work place injury

derives values from {0, 1, 2, 3, 4, 5,...}

means that there's a work place injury on the first day

and given that there's a 50% chance of a workplace injury on any given day,

means that there's no work place injury on the first day, but on the second day, there is. Hence,

This is the pmf for geometric random variable

The equation becomes,

Let μand μ

μ - μ =

since P + Q = 1

2. Probability that there will be an injury within the next 5 working days;

3.  Probability of winning if wager is placed on day 4,

option a is correct.

only one solution to the system of equations

step-by-step explanation:

if the graph of the equations do not intersects(i.,e if they are parallel) then, there are no solutions that are true for both the equations.

if the graph of the equations intersects, then there is one solution and that is true for both the equations.

since, in the given figure:

the two lines intersect each other

⇒there is only one solution which satisfy both the lines of an equations.

therefore, there is only one solution to the system of equation