Question

For what value of the constant , the real valued function :→ given by ()=+(−),−∞<<∞
where is a real parameter, is a probability density function for random variable

Answer 1

Answer:

The outcomes are measured, not counted.

The entire area under the curve and above the x-axis is equal to one.

Probability is found for intervals of x values rather than for individual x values.

P(c < x < d) is the probability that the random variable X is in the interval between the values c and d. P(c < x < d) is the area under the curve, above the x-axis, to the right of c and the left of d.

P(x = c) = 0 The probability that x takes on any single individual value is zero. The area below the curve, above the x-axis, and between x = c and x = c has no width, and therefore no area (area = 0). Since the probability is equal to the area, the probability is also zero.

P(c < x < d) is the same as P(c ≤ x ≤ d) because probability is equal to area.