The actual tracking weight of a stereo cartridge that is set to track at 3g on a particular changer can be regarded as a continuous random variable X with the following pdf. f(x) = Į k(1 – (x – 3)² ), 2sxs4, 0, otherwise. · 2.1. Find the value of k. ▪ 2.2. What is the probability that actual tracking weight is greater than the prescribed weight? ▪ 2.3. What is the probability that actual tracking weight is within 0.25g of the prescribed weight? 1 2.4. What is the probability that actual tracking weight differs from the prescribed weight by more than 0.5g?

This was what WAS given please helpppp

Let X be the total amount saved in dollars at the cash register. The pdf of X is given by: Value of X 20 28 40 50 58 70 probability 0.36 0.21 0.24 0.1225 0.0175 0.03 .0175 0.0025 Before I make the purchase, you would place my chance of saving $20 at 24%. Suppose you approach me after I pay for my items and ask: "Did you save any money?" If I answer "no", then you know I didn't save $20 and thus the chance of saving $20 changes from the unconditional chance 24% to the conditional chance 0%. However, if I answer "yes" my chance of saving $20 would get higher. What would be the conditional chance of saving $20 if you knew I got a discount? Mathematically, we seek: P(X = 20|X > 0 ). Even though it looks weird, it is just a conditional probability. Find it. P(X = 20|X > 0) = P(X = 20 and X > 0) / P(X > 0) = Hint: P(X = 20 and X > 0) be read off the table by identifying possible values where the event (X = 20 and X > 0) is true, don't use the multiplication rule. Do not round, express your…