Here are the steps to plot the fitted two-component normal mixture density on top of a histogram of the data points:

1. Load your data into R. Assuming your data is in the same directory as your R script:

```R
data

Question

Here are the steps to plot the fitted two-component normal mixture density on top of a histogram of the data points:

1. Load your data into R. Assuming your data is in the same directory as your R script:

```R
data <- read.csv("Data-A1a.csv")
```

2. Apply the EM algorithm to fit the two-component normal mixture density with common variances. The Mclust function in the mclust package will do this:

```R
model <- Mclust(data, G=2)
```

3. Calculate the number of bins for the histogram. You can use the formula given:

```R
n <- length(data)
bin_width <- 2 * IQR(data) / (n^(1/3))
range <- max(data) - min(data)
N <- ceiling(range / bin_width)
```

4. Plot the histogram of the data:

```R
hist(data, breaks=N, freq=FALSE, main="Histogram with Fitted Density")
```

The `freq=FALSE` argument ensures that the histogram is normalized, so it can be compared with the density.

5. Plot the fitted two-component normal mixture density on top of the histogram:

```R
x <- seq(min(data), max(data), length.out=100)
y <- densityMclust(model, x)$z
lines(x, y, col="red")
```

The `seq` function generates a sequence of x-values over the range of the data, and the `densityMclust` function calculates the corresponding y-values of the density. The `lines` function then adds these to the plot.

You should now see a plot of the histogram of the data with the fitted density overlaid. The density should give a good fit to the data if the model is appropriate.

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