Review of Probability

Expected Value: The expected value of a random variable Y, denoted E(Y), is the long-run average value of the random variable over many repeated trails or occurrences.

The expected value of a discrete random variable is computed as a weighted average of the possible outcomes of that random variable, where the weights are the probabilities of that outcome. The expected value of Y is called the expectation of Y or the mean of Y and is denoted Uy.

Example: Suppose you loan a friend $100 at 10% interest. There is a 99% chance that your loan will be repaid. That means, when your loan gets repaid, you receive $110 ($100 principal + $10 loan) amount. And, also, there is 1% chance that your friend defaults, and you get paid $0. Thus, on average, you would be repaid, $110*0.99 + $0*0.01 = $108.90.

Writing: Grammar Mistakes that I Did

As I am practicing grammar from a Writing SAT book, I feel that I should keep track of my grammar mistakes in a file. What better resources to do it than on my public blog? :D

• It's an error-free sentence. I found a mistake. Although I wish it were (A) otherwise (B), by this time next week I will have had surgery (C) on my knee, which was (D)injured during a hockey game last winter. No Error (E) 
• My mother is an extremely light (A) sleeper, and no matter how quiet (B) I come into the house at night after she has gone to bed, she hears me and calls out my name. No Error (E)
  
  The mistake lies in B, which has to be "quietly" in this context: the adverb modifying a verb. 

• When there was no error in this following sentence, I found one in there.
  
  E.g. Unsure whether the adoption agency would choose them, the Wilsons sought help from the court, which decided that their home would be suitable for the infant. No error (E)  
• Sandra, confident in (A) her creative ability, has enrolled (B) in the School of Design to study (C) painting, graphics, drawing, art history, and Architecture 101 (D). No error (E).
  
  It this sentence, D is an error. 
• If we (A) were to take him for (B) face value and not try to analyze, to dissect, and to explain possible ulterior motives, then I, for one(C), would (D) agree that he is telling the truth. No error (E).