A 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?
A) 0.7
B) 0.5
C) 0.4
D) 0.3
E) 0.6
c) .4
To find the mean value of a random variable, you need to multiply each possible outcome by its corresponding probability and sum them up.
In this case, the random variable X takes the value 0 if heads appear and 1 if tails appear. The probability of heads is 1 - 0.4 = 0.6, and the probability of tails is 0.4.
Mean value (μ) = (0 × probability of heads) + (1 × probability of tails)
= (0 × 0.6) + (1 × 0.4)
= 0 + 0.4
= 0.4
Therefore, the mean value of X is 0.4, which corresponds to option C.