stats true and false

For a discrete random variable, the sum of all values of its Probability Mass Function (PMF) over its entire range is always equal to 1, negative, and continuous.

• True

• False

The Cumulative Distribution Function (CDF) of any random variable is a non-decreasing function.

• False
• True

If two events A and B are dependent, then P(A∩B)=P(A)×P(B).

• True
• False

The variance of a random variable can never be negative, but the standard deviation can be.

• True

• False

For a continuous random variable, the value of the Probability Density Function (PDF) at any single point represents the probability of the variable taking that exact value.

• True

• False

In the binomial distribution, the probability of success p remains constant across all trials.

• True

• False

If the expected value of a random variable is zero, then the random variable itself must always take the value zero.

• True

• False

If a sequence of events is mutually exclusive, it means that they are independent of each other.

• True

• False

The CDF for any random variable X at negative infinity is always 0, and at positive infinity, it is always 1.

• True

• False