Way 2: Defining a new random variable X as the amount earned by the private debt collector per week. Then we can define X = + Y since X can be expressed as a linear function of Y. The probability distribution of X can be found as follows (start from the smallest realization of X):

For way 2, E(X) = $175

Step-by-step explanation:

Y is the number of loans collected in a week

given that $2000 is spent each week and charges $1500 per loan collected as service,

Therefore; the total amount earned (or lost) each week by the collector

X = -2000 + 1500*Y

In finding the probability distribution of X, the possible values of Y are 0,1,2 and 3

Thus, the possible values of X are:

when X = 0,  -2000 + 1500*0 = -2000

         X = 1,   -2000 + 1500*1 = -500

         X = 2,  -2000 + 1500*2 = 1000

         X = 3,  -2000 + 1500*3 = 2500.

Now, P(X = -2000) = P(-2000 + 1500*Y = -2000) = P(Y=0) = 0.15

          P(X = -500) = P(-2000 + 1500*Y = -500) = P(Y=1) = 0.40

          P(X = 1000) = P(-2000 + 1500*Y = 1000) = P(Y=2) = 0.30

          P(X = 2500) = P(-2000 + 1500*Y = 2500) = P(Y=3) = 0.15

Thus, the probability distribution of X is given by:

X  -2000-50010002500

p(x)   0.150.400.300.15

see in the workings below the expected value of X

E(X) = Σₓx * P ( X = x )

       = (-2000)*P(X=-2000) + (-500)*P(X=-500) + 1000*P(X=1000) + 2500*P(X=2500)

       = (-2000)*0.15 + (-500)*0.40 + 1000* 0.30 + 2500*0.15

       = -300 - 200 + 300 + 375

       = 175

i am unable to solve this problem

step-by-step explanation:

not only in mathematics, scientific proof also are required in the other field of science. also maths proofs are of particular structure, containing steps and logics. so proving is like doing science, it is science. that's why it is important to prove. 

an inaccurate proof leads to errors, or stating results that are not accurate.  which wil mess the probelm up you dont want this