A. Develop a probability distribution for x b. Compute the expected value of x
c. Compute the variance and standard deviation for x
d. Comment on what your results imply about wind conditions during boating accidents

a. The corresponding probabilities are obtained by converting the percentages into probabilities. That is, by dividing each value with 100.

F/N (where F =percentage of accidents and N =100)

Explanation:

 X01234

f(X)0.0960.570.2380.0770.019

b.  The formula for the expected value of a discrete random variable is E(x)= µ=∑xf(x)

XF(X)X.f(X)

00.0960

10.570.57

20.2380.476

30.0770.231

40.0190.076

Total         1      1.353

Hence, the value for expected value of X is 1.353

The formula for the variance of the discrete random variables is Var(x)= σ² =∑(x-µ)²f(x)

XF(X)(x-µ)(x-µ)²(x-µ)².f(x)

00.096-1.3531.83060.1757

10.57-0.3530.12460.0710

20.2380.6470.41860.0996

30.0771.6472.71260.2089

40.0192.6477.00660.1331

Total13.23512.09300.6884

Hence, the variance of the random variable x is 0.6884

The formula for the standard deviation of the discrete random variables is

σ=√(∑[(x-µ)².f(x)] )

Thus, the standard deviation is σ= √0.6884

                     =0.8297

Hence, the standard deviation of the random variable x is 0.8297  

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explanation:

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answer; sensory adaptation;