probability that a 2x2 matrix of numbers chosen from a set has a det of zero

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Probability Class - Undergraduate 400 Level

#23. You have $1000 and a certain commodity presently sells for $2 per ounce. Suppose that after one week the commodity will sell for either $1 or $4 an ounce, with these two probabilities being equally likely. (a) If your objective is to maximize the expected amount of money that you possess at the end of the week, what strategy should you employ? (b) If your objective is to maximize the expected amount of commodity that you possess at the end of the week, what strategy should you employ?

Probability Class - Undergraduate 400 Level

# 48. It is known that diskettes produced by a certain company will be defective with probability 0.01, independently of each other. The company sells the diskettes in packages of size 10 and offers a money-back guarantee that at most 1 of 10 diskettes in the package will be defective. If someone buys 3 packages, what is the probability that he or she will return exactly one of them?

Probability Class - Undergraduate 400 Level

# 3. Consider the function f (x) = C ( 2x - x³) 0 < x < 5/2 f (x) = 0 otherwise. Could f be a probability density function? If so, determine C. Repeat if f (x) were given by f (x) = C ( 2x - x²) 0 < x < 5/2 f (x) = 0 otherwise.

The problem is from probability class.

The probability density function of X, the lifetime of a certain type of electronic device (measured in hours), is given by ... (see attachment)