Let us suppose that some article studied the probability of death due to burn in

Question

Let us suppose that some article studied the probability of death due to burn injuries. The identified risk factors in this study are age greater than 60 years, burn injury in more than 40% of body-surface area, and presence of inhalation injury. It is estimated that the probability of death is 0.003, 0.03, 0.33, or 0.82, if the injured person has zero, one, two, or three risk factors, respectively. Suppose that three people are injured in a fire and treated independently. Among these three people, two people have one risk factor and one person has three risk factors. Let the random variable X denote number of deaths in this fire. Determine the probability mass function of X Calculate the mean and variance for the random variable X Mean Variance -

Explanation / Answer

let X1 and X2 is for first 2 persons with one injury and X3 for 3rd person with 3 injury

here mean =E(X) =E(X1+X2+X3)=E(X1)+E(X2)+E(X3) =0.03+0.03+0.82=0.88

Variance =Var(X1)+Var(X2)+var(X3)=0.03*(1-0.03)+0.03*(1-0.03)+0.82*(1-0.82)=0.2058

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