1
JEE Main 2024 (Online) 5th April Evening Shift
Numerical
+4
-1
Change Language

Let the mean and the standard deviation of the probability distribution

$$\mathrm{X}$$ $$\alpha$$ 1 0 $$-$$3
$$\mathrm{P(X)}$$ $$\frac{1}{3}$$ $$\mathrm{K}$$ $$\frac{1}{6}$$ $$\frac{1}{4}$$

be $$\mu$$ and $$\sigma$$, respectively. If $$\sigma-\mu=2$$, then $$\sigma+\mu$$ is equal to ________.

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2
JEE Main 2024 (Online) 30th January Evening Shift
Numerical
+4
-1
Change Language

The variance $$\sigma^2$$ of the data

$$x_i$$ 0 1 5 6 10 12 17
$$f_i$$ 3 2 3 2 6 3 3

is _________.

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3
JEE Main 2024 (Online) 29th January Morning Shift
Numerical
+4
-1
Change Language

If the mean and variance of the data $$65,68,58,44,48,45,60, \alpha, \beta, 60$$ where $$\alpha> \beta$$, are 56 and 66.2 respectively, then $$\alpha^2+\beta^2$$ is equal to _________.

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4
JEE Main 2024 (Online) 27th January Evening Shift
Numerical
+4
-1
Change Language

The mean and standard deviation of 15 observations were found to be 12 and 3 respectively. On rechecking it was found that an observation was read as 10 in place of 12 . If $$\mu$$ and $$\sigma^2$$ denote the mean and variance of the correct observations respectively, then $$15\left(\mu+\mu^2+\sigma^2\right)$$ is equal to __________.

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