Random Variables And Its Probability Distributions

Step 1: Understanding the Concept:
Mean of a frequency distribution is . Median is the value corresponding to the cumulative frequency .
: Key Formula or Approach:
The -th value is for with frequency .
Using identity .
Step 2: Detailed Explanation:
Sum of frequencies .
.
Mean .
Total observations .
Cumulative frequency reaches half at (middle of binomial expansion).
Median value is .
Step 3: Final Answer:
The median is 56.

Step 1: Understanding the Concept:
We first find the point of intersection of the two given lines. Then, we write the equation of a general line passing through this point. By finding where this line intersects the and axes, we can determine the coordinates of and and subsequently the locus of their midpoint .
Step 2: Key Formula or Approach:
1. Intersection: Solve the system of linear equations.
2. Intercept form of a line: , where and .
3. Midpoint : and .
Step 3: Detailed Explanation:
Solving and : Subtracting the equations gives . Substituting into the first: . The point of intersection is . Let the line be . Since it passes through : Let the midpoint be . Then and . Substituting these into the equation: Replacing with , we get .
Step 4: Final Answer:
The locus of the midpoint is .