A coin tossed twice. Let X denote the number of tails on the first toss and Y denote nber of tails on the 2 tosses. If the coin is unbalanced and a tail has a AB% chance of nd; int probability distribution table of X and Y with their marginal distributions. robability that at least 1 tail occurs. the conditional distribution of X given Y=1. tod valu e of V
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
![Question 2: A coin tossed twice. Let X denote the number of tails on the first toss and Y denote
the total number of tails on the 2 tosses. If the coin is unbalanced and a tail has a AB% chance of
occurring. Find;
a. the joint probability distribution table of X and Y with their marginal distributions.
b. the probability that at least 1 tail occurs.
c. Find the conditional distribution of X given Y=1.
d. Find the expected value of X.
e. Find the standard deviation of X.
f. Find the covariance of X and Y.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7404b8e3-24ff-42f9-8321-7840763728c2%2Fa75c1c64-852a-4f13-8571-4a08157b24be%2Fbjjknsi_processed.png&w=3840&q=75)
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