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4. When you toss 5 coins once, if the number of head(s) is the random variable define on the resulting sample space. What is the set of random variable resulting from this experiment?

5.Let X have a standard gamma distribution with alpha =7. Compute P(X <4 or X>6)

6. If x is a normal variable with the mean u=5 and variance (sigma square)=16, what is the probability that x is less than or equal to 6?

7. Let X have a uniform distribution on the interval [A,B]. compute V(X)

8. Components of a certain type are shipped to a supplier in batches of ten. Suppose that 50% of all such batches contain no defective components. 30% contain one defective component, and 20% contain two defective components. Two components from a batch are randomly selected and tested. What are the probabilities associated with 0.1, and 2 defective components being in the batch under the condition that neither tested component is defective
Discuss the differentiation of function like KX and log X.
1. A certain shop repairs both audio and video components. Let A denote the event that the next component brought in for repair is an audio component, and let B be the event that the next component is a compact disc player (so the event B is contained in A). Suppose that P(A)= 0.6 and P(B) =0.05. What is P(B|A)?

2.Each of 12 refrigerators of a certain type has been returned to a distributor because of an audible, high-pitched, oscillating noise when the refrigerator is running. Suppose that 7 of these refrigerator have defective compressor and the other 5 have less serious problems. If the refrigerators are examined in random order. Let X be the number among the first 6 examined that have a defective compressor. What is the probability that X exceeds its mean value by more than 1 standard deviation?

3. Evaluate (x-2)!(y-4) if x=6 and y=9
Rossdale, Inc., had additions to retained earnings for the year just ended of $636,000. The firm paid out $75,000 in cash dividends, and it has ending total equity of $7.31 million.

If the company currently has 680,000 shares of common stock outstanding, what are earnings per share? Dividends per share? What is book value per share? (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.)
Example of a subset of a set that's contains 4element
Find the magnitude of vector a=3i-2j+2k
If a and b are non-collinear vectors and A=(x+y)a + (2x+y+1) b,find x and y
3. The FBI database IAFIS holds records of over 51 million criminal 10-print fingerprint records, each of them theoretically unique. When analyzing fingerprints, there are specific points on each fingerprint that are utilized to distinguish and identify a fingerprint with a database match. Commonly 10 to 12 matching points are used to affect a match, but there is no standard rule to this.
On average per month, a particular laboratory uses 15 points to identify and match a fingerprint from a crime scene with a suspect in the database. Calculate the following probabilities:
a. The probability of a successful match in a given month with 6 points of identification.
b. The probability of a successful match in a given month with either 12 or 17 points of identification.
Fit a normal curve to the following data
x: 2 4 6 8 10
f: 1 4 6 4 1
Evaluate Integration of (x^2cosx dx) from '0 to π/2'
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