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Self Assessment/ student activity
1. A continuous random variable X that can assume values between x =
1 and x = 3 has a density function given by f (x) = 1/2. (a) Show that the
area under the curve is equal to 1. (b) Find P (2 <X < 2.5). (c) Find P
(X ≤ 1.6)
2. A continuous random variable X that can assume values between x = 2
and x = 5 has a density function given by f (x) = 2(1 +x)/27.
Find (a) P(X < 4); (b) P (3 ≤ X < 4)
3. From a box containing 4 dimes and 2 nickels, 3 coins are selected at
random without replacement. Find the probability distribution for the total
T of the 3 coins. Express the probability distribution graphi- cally as a
probability histogram.
4. From a box containing 4 black balls and 2 green balls, 3 balls are drawn in
succession, each ball being replaced in the box before the next draw is made.
Find the probability distribution for the number of green balls.
Consider two normalized eigen functions and , corresponding to the same eigen value. If
Integral a1a2*dT = d
where is real
Find a normalized linear combinations of and that are orthogonal to
(a) a1
(b) a1+a2
Note: The coefficients of the linear combinations need not be real
Self Assessment/ student activity
1. A continuous random variable X that can assume values between x =
1 and x = 3 has a density function given by f (x) = 1/2. (a) Show that the
area under the curve is equal to 1. (b) Find P (2 <X < 2.5). (c) Find P
(X ≤ 1.6)
2. A continuous random variable X that can assume values between x = 2
and x = 5 has a density function given by f (x) = 2(1 +x)/27.
Find (a) P(X < 4); (b) P (3 ≤ X < 4)
3. From a box containing 4 dimes and 2 nickels, 3 coins are selected at
random without replacement. Find the probability distribution for the total
T of the 3 coins. Express the probability distribution graphi- cally as a
probability histogram.
4. From a box containing 4 black balls and 2 green balls, 3 balls are drawn in
succession, each ball being replaced in the box before the next draw is made.
Find the probability distribution for the number of green balls.
5. Discuss some of the important criticisms of the forecasting ability of the leading economic
indicators.
2. Enumerate methods of qualitative and quantitative forecasting. What are the major differ-
ences between the two?
1-5. Two point charges, q1 = 8 µC and q2 = -5 µC, are separated by a distance r = 0.1 m. What is the magnitude of the electric force? Note: 1 µC = 10-6 C.
1. Explain the difference between time series data and cross-sectional data. Provide examples
of each type of data.
Find the mean of the probability distribution of a random variable X which if 𝑃(𝑋) =
𝑥+1
20
for X= 1, 2, 3, 4, and 5.
Find the mean of the probability distribution of a random variable X which if
P(X)=1/10 for X=1, 2, 3, …, 10.
Find the mean of the probability distribution of a random variable X which can take
only the values 2, 4, 5, and 9, given that P(2)=9/20, P(5)=1/20, P(5)=1/5, and
P(9)=3/10.
#339914 on Dec 2023