An article in Knee Surgery, Sports Traumatology, Arthroscopy, \"Arthroscopic men

Question

An article in Knee Surgery, Sports Traumatology, Arthroscopy, "Arthroscopic meniscal repair with an absorbable screw: results and surgical technique," (2005, Vol. 13, pp, 273-279) cites a success rate more than 90% for meniscal tears with a rim width of less than 3 mm, but only a 67% success rate for tears of 3-6 mm. If you are unlucky enough to suffer a meniscal tear of less than 3 mm on your left knee, and one of width 3-6 mm on your right knee, what are the mean and variance of the number of successful surgeries? Assume the surgeries are independent. Round your answers to three decimal places (e.g. 98.765) Mean = variance =

Explanation / Answer

Solution-

Let us denote the number of successfull surgery in left knee by random variable X which must follow bernoulli distribution with parameter -

p = 0.9

Also, Let us denote the number of successfull surgery in left knee by random variable Y which must follow bernoulli distribution with parameter -

p = 0.67

E(X+Y) = E(X) + E(Y)

= 0.9 + 0.67

Var(X+Y) = var(X) + var(Y)

= 0.9 * 0.1 + 0.67 * 0.33

= 0.3111

Answers

TY!

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