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Find the lim r ̄(t), where t→1
sin(3t−3) r ̄(t)= t3, t−1 ,e2t
E=k•10+1
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.
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.
11^3+4t= p(mod 10)
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.
Find the mean of the probability distribution of a random variable X which can take
only the values 3, 5, and 7, given that P(3)=7/30, P(5)= 1/3, and P(7)=13/30
Find the mean of the probability distribution of a random variable X which can take
only the values 1, 2, and 3, given that P(1)=10/33, P(2)= 1/3, and P(3)=1/33
#339914 on Dec 2023