Determine the mean and variance of the random variable in Exercise 3-23.

3-23. An article in Knee Surgery, Sports Traumatology, Arthroscopy [“Arthroscopy Meniscal Repair with an Absorbable Screw: Results and Surgical Technique” (2005, Vol. 13, pp 273-279)] cities a success rate more than 90% for meniscal tears with a rim width under 3mm, but only a 67% success rate for tears of 3-6mm. If you are unlucky enough to suffer a meniscal tear of under 3mm on your left knee and one of width 3-6 mm on your right, what is the probability mass function of the number of successful surgeries? Assume that the surgeries are independent.

Solution:

Step 1 of 3:

We have the success rate more than 90% for meniscal tears with a rim width under 3mm,

But only 67% success rate for tears of 3-6mm.

The claim is to find the mean and variance.