Biased coin has a 0.4 probability of landing on tails. The random variable x, based on a single toss of the coin, is defined as follows: x=0 if heads appears; x=1 if tails appears. What Is the mean value of X?
Is it .
0.3
.4
.6
.5
.7
For each coin toss, the probability of x=1 is 0.4.
The mean value of X for n tries is :
(0.4(1)*n)/n = 0.4
To find the mean value of a random variable, you need to calculate the expected value. In this case, we have a biased coin with a 0.4 probability of landing on tails (1) and a 0.6 probability of landing on heads (0).
The mean value of a random variable X is denoted as E(X) or μ (mu). It is calculated by multiplying each possible value of X by its respective probability and summing up these products.
In this scenario, we have two possible values of X: 0 and 1.
E(X) = (0 * P(X = 0)) + (1 * P(X = 1))
The probability of X being 0 (P(X = 0)) is the probability of getting heads, which is 0.6.
The probability of X being 1 (P(X = 1)) is the probability of getting tails, which is 0.4.
E(X) = (0 * 0.6) + (1 * 0.4)
= 0 + 0.4
= 0.4
Therefore, the mean value of the random variable X is 0.4.
Out of the given options, the correct answer is 0.4.