A prisoner is trapped in a cell containing three doors. The first door leads to a tunnel that returns him to his cell after two days of travel. The second leads to a tunnel that returns him to his cell after three days of travel. The third door leads immediately to freedom. Let X=the number of days until theprisoner reaches freedom.

a. Assuming that the prisoner will always select doors 1, 2, and 3 with probabilities 0.5, 0.3, 0.2, make an argument that X is a proper random variable (i. e. the prisoner will not be trapped in his cell forever.). Additionally, what is the expected number of days until he reaches freedom?

b. Assuming that the prisoner is always equally likely to choose among those door that he has not used, what is the expected number of days until he reaches freedom? (In this version, for instance, if the prisoner initially tries door 1, then when he returns to the cell, he will now select only from doors 2 and 3.)

c. For parts (a) and (b) find the variance of the number of days until the prisoner reaches freedom.

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is

you are uyytr tyy

step-by-step explanation:

answer: 33 ( approx)

step-by-step explanation:

since, in the linear regression formula, the slope is the a in the equation y = b + ax ( by comparing it with the general equation of line y = mx + c )

where,

here given table is,

price ($), x   :           18         23       25       29       30       33

pairs sold, y :         16         13         10       8         6       2

so, ,   ,   ,

and   ,

thus, slop of the given line is,

⇒  

⇒   ≈ 33

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